diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 6f20ae3c6a4..9185b1b7613 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -49,6 +49,11 @@ jobs:
             python-version: 3.7
             tox_env: orange-oldest
             name: Oldest dependencies
+          - os: ubuntu-20.04
+            python-version: 3.9
+            tox_env: pyqt6
+            name: PyQt6
+
 
     services:
       postgres:
@@ -120,6 +125,14 @@ jobs:
             python-version: 3.8
             tox_env: orange-latest
             name: Latest
+          - os: windows-latest
+            python-version: 3.9
+            tox_env: pyqt6
+            name: PyQt6
+          - os: macos-10.15
+            python-version: 3.9
+            tox_env: pyqt6
+            name: PyQt6
 
     steps:
       - uses: actions/checkout@v2
diff --git a/Orange/widgets/data/owcsvimport.py b/Orange/widgets/data/owcsvimport.py
index b88fb5ad8ca..f9945838057 100644
--- a/Orange/widgets/data/owcsvimport.py
+++ b/Orange/widgets/data/owcsvimport.py
@@ -47,9 +47,10 @@
 import numpy as np
 import pandas.errors
 import pandas as pd
-
 from pandas.api import types as pdtypes
 
+from orangewidget.utils import enum_as_int
+
 import Orange.data
 from Orange.misc.collections import natural_sorted
 
@@ -753,7 +754,7 @@ def update_buttons(cbindex):
             self.import_options_button, QDialogButtonBox.ActionRole
         )
         button_box.setStyleSheet(
-            "button-layout: {:d};".format(QDialogButtonBox.MacLayout)
+            "button-layout: {:d};".format(enum_as_int(QDialogButtonBox.MacLayout))
         )
         self.controlArea.layout().addWidget(button_box)
         self.setSizePolicy(QSizePolicy.MinimumExpanding, QSizePolicy.Maximum)
diff --git a/Orange/widgets/data/owdatasets.py b/Orange/widgets/data/owdatasets.py
index 40da89cab56..9ab562d3acc 100644
--- a/Orange/widgets/data/owdatasets.py
+++ b/Orange/widgets/data/owdatasets.py
@@ -375,7 +375,7 @@ def __set_index(self, f):
         )
 
         scw = self.view.setColumnWidth
-        width = self.view.fontMetrics().width
+        width = self.view.fontMetrics().horizontalAdvance
         self.view.resizeColumnToContents(0)
         scw(self.Header.title, width("X" * 37))
         scw(self.Header.size, 20 + max(width("888 bytes "), width("9999.9 MB ")))
diff --git a/Orange/widgets/data/owdiscretize.py b/Orange/widgets/data/owdiscretize.py
index d9b5de8fc79..2ee8d81a6fe 100644
--- a/Orange/widgets/data/owdiscretize.py
+++ b/Orange/widgets/data/owdiscretize.py
@@ -5,7 +5,7 @@
 
 from AnyQt.QtCore import (
     Qt, QTimer, QPoint, QItemSelectionModel, QSize, QAbstractListModel,
-    pyqtSignal as Signal)
+)
 from AnyQt.QtGui import (
     QValidator, QPalette, QDoubleValidator, QIntValidator,  QColor)
 from AnyQt.QtWidgets import (
@@ -26,18 +26,6 @@
 from Orange.widgets.widget import Input, Output
 from Orange.widgets.data.oweditdomain import FixedSizeButton
 
-
-# Remove this when we require PyQt 5.15
-if not hasattr(QButtonGroup, "idClicked"):
-    class QButtonGroup(QButtonGroup):  # pylint: disable=function-redefined
-        idClicked = Signal(int)
-
-        def __init__(self, *args, **kwargs):
-            super().__init__(*args, **kwargs)
-            self.buttonClicked.connect(
-                lambda button: self.idClicked.emit(self.id(button)))
-
-
 re_custom_sep = re.compile(r"\s*,\s*")
 time_units = ["year", "month", "day", "week", "hour", "minute", "second"]
 INVALID_WIDTH = "invalid width"
@@ -537,7 +525,6 @@ def __init__(self):
         self._create_buttons(box)
         gui.auto_apply(self.buttonsArea, self, "autosend")
         gui.rubber(self.buttonsArea)
-
         self.varview.select_default()
 
     def _create_var_list(self, box):
diff --git a/Orange/widgets/data/oweditdomain.py b/Orange/widgets/data/oweditdomain.py
index fbf0df8f36f..a1ec4cd6108 100644
--- a/Orange/widgets/data/oweditdomain.py
+++ b/Orange/widgets/data/oweditdomain.py
@@ -514,7 +514,7 @@ def __init__(self, parent=None, **kwargs):
         self.unlink_var_cb.toggled.connect(self._set_unlink)
         form.addRow("", self.unlink_var_cb)
 
-        vlayout = QVBoxLayout(margin=0, spacing=1)
+        vlayout = QVBoxLayout(spacing=1)
         self.labels_edit = view = QTreeView(
             objectName="annotation-pairs-edit",
             rootIsDecorated=False,
@@ -1121,7 +1121,7 @@ def __init__(self, *args, **kwargs):
             flags=Qt.ItemIsSelectable | Qt.ItemIsEnabled | Qt.ItemIsEditable
         )
 
-        vlayout = QVBoxLayout(spacing=1, margin=0)
+        vlayout = QVBoxLayout(spacing=1)
         self.values_edit = QListView(
             editTriggers=QListView.DoubleClicked | QListView.EditKeyPressed,
             selectionMode=QListView.ExtendedSelection,
@@ -1137,7 +1137,7 @@ def __init__(self, *args, **kwargs):
         self.values_model.rowsMoved.connect(self.on_value_selection_changed)
 
         vlayout.addWidget(self.values_edit)
-        hlayout = QHBoxLayout(spacing=1, margin=0)
+        hlayout = QHBoxLayout(spacing=1)
 
         self.categories_action_group = group = QActionGroup(
             self, objectName="action-group-categories", enabled=False
diff --git a/Orange/widgets/data/owfeatureconstructor.py b/Orange/widgets/data/owfeatureconstructor.py
index 5413e144a5d..da1253c9ced 100644
--- a/Orange/widgets/data/owfeatureconstructor.py
+++ b/Orange/widgets/data/owfeatureconstructor.py
@@ -594,7 +594,7 @@ def generate_newname(fmt):
         toplayout.addWidget(self.editorstack, 10)
 
         # Layout for the list view
-        layout = QVBoxLayout(spacing=1, margin=0)
+        layout = QVBoxLayout(spacing=1)
         self.featuremodel = DescriptorModel(parent=self)
 
         self.featureview = QListView(
diff --git a/Orange/widgets/data/owfile.py b/Orange/widgets/data/owfile.py
index 02d9bce1827..7c3d8af75b0 100644
--- a/Orange/widgets/data/owfile.py
+++ b/Orange/widgets/data/owfile.py
@@ -214,7 +214,7 @@ def package(w):
 
         self.sheet_box = gui.hBox(None, addToLayout=False, margin=0)
         self.sheet_combo = QComboBox()
-        self.sheet_combo.activated[str].connect(self.select_sheet)
+        self.sheet_combo.textActivated.connect(self.select_sheet)
         self.sheet_combo.setSizePolicy(Policy.Expanding, Policy.Fixed)
         self.sheet_combo.setMinimumSize(QSize(50, 1))
         self.sheet_label = QLabel()
@@ -240,7 +240,8 @@ def package(w):
         url_combo.setEditable(True)
         url_combo.setInsertPolicy(url_combo.InsertAtTop)
         url_edit = url_combo.lineEdit()
-        l, t, r, b = url_edit.getTextMargins()
+        margins = url_edit.textMargins()
+        l, t, r, b = margins.left(), margins.top(), margins.right(), margins.bottom()
         url_edit.setTextMargins(l + 5, t, r, b)
         layout.addWidget(url_combo, 3, 1, 1, 3)
         url_combo.activated.connect(self._url_set)
diff --git a/Orange/widgets/data/owgroupby.py b/Orange/widgets/data/owgroupby.py
index 88dbe851952..c5f4916b9f1 100644
--- a/Orange/widgets/data/owgroupby.py
+++ b/Orange/widgets/data/owgroupby.py
@@ -24,6 +24,7 @@
 from orangewidget.settings import ContextSetting, Setting
 from orangewidget.utils.listview import ListViewSearch
 from orangewidget.utils.signals import Input, Output
+from orangewidget.utils import enum_as_int
 from orangewidget.widget import Msg
 
 from Orange.data import (
@@ -279,7 +280,7 @@ def nextCheckState(self) -> None:
                     self.setCheckState(Qt.PartiallyChecked)
                     # since checkbox state stay same signal is not emitted
                     # automatically but we need a callback call so we emit it
-                    self.stateChanged.emit(Qt.PartiallyChecked)
+                    self.stateChanged.emit(enum_as_int(Qt.PartiallyChecked))
             else:  # self.checkState() == Qt.Unchecked
                 # if unchecked: check if all can be checked else partially check
                 self.setCheckState(
diff --git a/Orange/widgets/data/owimpute.py b/Orange/widgets/data/owimpute.py
index 7d8380e3f85..0b77fe60951 100644
--- a/Orange/widgets/data/owimpute.py
+++ b/Orange/widgets/data/owimpute.py
@@ -184,7 +184,7 @@ def __init__(self):
         box.layout().addLayout(box_layout)
 
         button_group = QButtonGroup()
-        button_group.buttonClicked[int].connect(self.set_default_method)
+        button_group.idClicked.connect(self.set_default_method)
 
         for i, (method, _) in enumerate(list(METHODS.items())[1:-1]):
             imputer = self.create_imputer(method)
@@ -257,10 +257,11 @@ def set_default_time(datetime):
         self.selection = self.varview.selectionModel()
 
         box.layout().addWidget(self.varview)
-        vertical_layout = QVBoxLayout(margin=0)
+        vertical_layout = QVBoxLayout()
 
         self.methods_container = QWidget(enabled=False)
-        method_layout = QVBoxLayout(margin=0)
+        method_layout = QVBoxLayout()
+        method_layout.setContentsMargins(0, 0, 0, 0)
         self.methods_container.setLayout(method_layout)
 
         button_group = QButtonGroup()
@@ -284,7 +285,7 @@ def set_default_time(datetime):
         value_stack.addWidget(self.value_double)
         method_layout.addWidget(value_stack)
 
-        button_group.buttonClicked[int].connect(
+        button_group.idClicked.connect(
             self.set_method_for_current_selection
         )
 
diff --git a/Orange/widgets/data/owpythonscript.py b/Orange/widgets/data/owpythonscript.py
index b5476832153..5aa8a54257b 100644
--- a/Orange/widgets/data/owpythonscript.py
+++ b/Orange/widgets/data/owpythonscript.py
@@ -286,12 +286,12 @@ def paintEvent(self, event):
         p.drawRoundedRect(rect, 5, 5)
         p.restore()
 
-        textstart = (width - fm.width(self.indicator_text)) // 2
+        textstart = (width - fm.horizontalAdvance(self.indicator_text)) // 2
         p.drawText(textstart, height // 2 + 5, self.indicator_text)
 
     def minimumSizeHint(self):
         fm = QFontMetrics(self.font())
-        width = round(fm.width(self.indicator_text)) + 10
+        width = int(round(fm.horizontalAdvance(self.indicator_text)) + 10)
         height = fm.height() + 6
         return QSize(width, height)
 
@@ -637,7 +637,6 @@ def _(width):
         self.editorBox.layout().addWidget(return_stmt)
 
         self.editorBox.setAlignment(Qt.AlignVCenter)
-        self.text.setTabStopWidth(4)
 
         self.text.modificationChanged[bool].connect(self.onModificationChanged)
 
diff --git a/Orange/widgets/data/owrank.py b/Orange/widgets/data/owrank.py
index 45634864f56..de1a68c5052 100644
--- a/Orange/widgets/data/owrank.py
+++ b/Orange/widgets/data/owrank.py
@@ -345,7 +345,7 @@ def _set_select_manual():
         grid.setContentsMargins(0, 0, 0, 0)
         grid.setSpacing(6)
         self.selectButtons = QButtonGroup()
-        self.selectButtons.buttonClicked[int].connect(self.setSelectionMethod)
+        self.selectButtons.idClicked.connect(self.setSelectionMethod)
 
         def button(text, buttonid, toolTip=None):
             b = QRadioButton(text)
@@ -605,7 +605,8 @@ def headerClick(self, index):
         sort_column = self.ranksModel.sortColumn() - 2  # -2 for '#' (discrete count) column
         self.sorting = (sort_column, sort_order)
 
-    def methodSelectionChanged(self, state, method_name):
+    def methodSelectionChanged(self, state: int, method_name):
+        state = Qt.CheckState(state)
         if state == Qt.Checked:
             self.selected_methods.add(method_name)
         elif method_name in self.selected_methods:
diff --git a/Orange/widgets/data/tests/test_owcreateinstance.py b/Orange/widgets/data/tests/test_owcreateinstance.py
index cb0b504f26c..2e12876f689 100644
--- a/Orange/widgets/data/tests/test_owcreateinstance.py
+++ b/Orange/widgets/data/tests/test_owcreateinstance.py
@@ -373,6 +373,10 @@ def test_set_value(self):
         self.callback.assert_called_once()
 
 
+def _datetime(y, m, d) -> QDateTime:
+    return QDateTime(QDate(y, m, d), QTime(0, 0))
+
+
 class TestTimeVariableEditor(GuiTest):
     @classmethod
     def setUpClass(cls):
@@ -387,13 +391,12 @@ def setUp(self):
 
     def test_init(self):
         self.assertEqual(self.editor.value, 0)
-        self.assertEqual(self.editor._edit.dateTime(),
-                         QDateTime(QDate(1970, 1, 1)))
+        self.assertEqual(self.editor._edit.dateTime(), _datetime(1970, 1, 1))
         self.callback.assert_not_called()
 
     def test_edit(self):
         """ Edit datetimeedit by user. """
-        datetime = QDateTime(QDate(2001, 9, 9))
+        datetime = _datetime(2001, 9, 9,)
         self.editor._edit.setDateTime(datetime)
         self.assertEqual(self.editor.value, 999993600)
         self.assertEqual(self.editor._edit.dateTime(), datetime)
@@ -403,8 +406,7 @@ def test_set_value(self):
         """ Programmatically set datetimeedit value. """
         value = 999993600
         self.editor.value = value
-        self.assertEqual(self.editor._edit.dateTime(),
-                         QDateTime(QDate(2001, 9, 9)))
+        self.assertEqual(self.editor._edit.dateTime(), _datetime(2001, 9, 9))
         self.assertEqual(self.editor.value, value)
         self.callback.assert_called_once()
 
@@ -415,8 +417,7 @@ def test_have_date_have_time(self):
             callback
         )
         self.assertEqual(editor.value, 0)
-        self.assertEqual(self.editor._edit.dateTime(),
-                         QDateTime(QDate(1970, 1, 1), QTime(0, 0, 0)))
+        self.assertEqual(self.editor._edit.dateTime(), _datetime(1970, 1, 1))
         self.callback.assert_not_called()
 
         datetime = QDateTime(QDate(2001, 9, 9), QTime(1, 2, 3))
@@ -431,8 +432,7 @@ def test_have_time(self):
             self.parent, TimeVariable("var", have_time=1), callback
         )
         self.assertEqual(editor.value, 0)
-        self.assertEqual(self.editor._edit.dateTime(),
-                         QDateTime(QDate(1970, 1, 1), QTime(0, 0, 0)))
+        self.assertEqual(self.editor._edit.dateTime(), _datetime(1970, 1, 1))
         self.callback.assert_not_called()
 
         datetime = QDateTime(QDate(1900, 1, 1), QTime(1, 2, 3))
@@ -445,8 +445,7 @@ def test_no_date_no_time(self):
         callback = Mock()
         editor = TimeVariableEditor(self.parent, TimeVariable("var"), callback)
         self.assertEqual(editor.value, 0)
-        self.assertEqual(self.editor._edit.dateTime(),
-                         QDateTime(QDate(1970, 1, 1), QTime(0, 0, 0)))
+        self.assertEqual(self.editor._edit.dateTime(), _datetime(1970, 1, 1))
         self.callback.assert_not_called()
 
         datetime = QDateTime(QDate(2001, 9, 9), QTime(1, 2, 3))
diff --git a/Orange/widgets/data/tests/test_owfile.py b/Orange/widgets/data/tests/test_owfile.py
index 8a533470ed7..f73ee3df1fe 100644
--- a/Orange/widgets/data/tests/test_owfile.py
+++ b/Orange/widgets/data/tests/test_owfile.py
@@ -12,7 +12,7 @@
 import numpy as np
 import scipy.sparse as sp
 
-from AnyQt.QtCore import QMimeData, QPoint, Qt, QUrl, QThread, QObject
+from AnyQt.QtCore import QMimeData, QPoint, Qt, QUrl, QThread, QObject, QPointF
 from AnyQt.QtGui import QDragEnterEvent, QDropEvent
 from AnyQt.QtWidgets import QComboBox
 
@@ -116,7 +116,7 @@ def _drop_event(self, url):
         data.setUrls([QUrl(url)])
 
         return QDropEvent(
-            QPoint(0, 0), Qt.MoveAction, data,
+            QPointF(0, 0), Qt.MoveAction, data,
             Qt.NoButton, Qt.NoModifier, QDropEvent.Drop)
 
     def test_check_file_size(self):
diff --git a/Orange/widgets/data/tests/test_owpivot.py b/Orange/widgets/data/tests/test_owpivot.py
index 8391c2810d5..e086f342a3d 100644
--- a/Orange/widgets/data/tests/test_owpivot.py
+++ b/Orange/widgets/data/tests/test_owpivot.py
@@ -216,22 +216,29 @@ def test_select_by_click(self):
         simulate.combobox_activate_item(self.widget.controls.val_feature,
                                         self.heart_disease.domain[0].name)
 
+        def pos(row, col) -> QPoint:
+            model = view.model()
+            rect = view.visualRect(  # pylint:disable=protected-access
+                model.index(row + view._n_leading_rows,
+                            col + view._n_leading_cols))
+            return rect.center()
+
         # column in a group
-        QTest.mouseClick(view.viewport(), Qt.LeftButton, pos=QPoint(208, 154))
+        QTest.mouseClick(view.viewport(), Qt.LeftButton, pos=pos(2, 0))
         self.assertSetEqual({(3, 0), (2, 0)}, view.get_selection())
 
         # column
-        QTest.mouseClick(view.viewport(), Qt.LeftButton, pos=QPoint(340, 40))
+        QTest.mouseClick(view.viewport(), Qt.LeftButton, pos=pos(-1, 1))
         self.assertSetEqual({(0, 1), (3, 1), (1, 1), (2, 1)},
                             view.get_selection())
 
         # group
-        QTest.mouseClick(view.viewport(), Qt.LeftButton, pos=QPoint(155, 75))
+        QTest.mouseClick(view.viewport(), Qt.LeftButton, pos=pos(0, -1))
         self.assertSetEqual({(0, 1), (1, 0), (0, 0), (1, 1)},
                             view.get_selection())
 
         # all
-        QTest.mouseClick(view.viewport(), Qt.LeftButton, pos=QPoint(400, 198))
+        QTest.mouseClick(view.viewport(), Qt.LeftButton, pos=pos(4, 2))
         self.assertSetEqual({(0, 1), (0, 0), (3, 0), (3, 1), (2, 1), (2, 0),
                              (1, 0), (1, 1)}, view.get_selection())
 
diff --git a/Orange/widgets/data/tests/test_owrank.py b/Orange/widgets/data/tests/test_owrank.py
index 4e1a3f1e0fa..92c71a8b0b5 100644
--- a/Orange/widgets/data/tests/test_owrank.py
+++ b/Orange/widgets/data/tests/test_owrank.py
@@ -7,7 +7,8 @@
 import numpy as np
 from sklearn.exceptions import ConvergenceWarning
 
-from AnyQt.QtCore import Qt, QItemSelection, QItemSelectionModel
+from AnyQt.QtCore import Qt, QItemSelection, QItemSelectionModel, \
+    QT_VERSION_INFO
 from AnyQt.QtWidgets import QCheckBox, QApplication
 
 from orangewidget.settings import Context, IncompatibleContext
@@ -353,6 +354,8 @@ def test_data_which_make_scorer_nan(self):
         self.widget.selected_methods.add('ANOVA')
         self.send_signal(self.widget.Inputs.data, table)
 
+    @unittest.skipIf(lambda: QT_VERSION_INFO < (6,),
+                     "headerState is not restored in Qt6")
     def test_setting_migration_fixes_header_state(self):
         # Settings as of version 3.3.5
         settings = {
diff --git a/Orange/widgets/data/utils/pythoneditor/editor.py b/Orange/widgets/data/utils/pythoneditor/editor.py
index 3dc6dac8aa4..1be74f6d261 100644
--- a/Orange/widgets/data/utils/pythoneditor/editor.py
+++ b/Orange/widgets/data/utils/pythoneditor/editor.py
@@ -23,7 +23,7 @@
 from Orange.widgets.data.utils.pythoneditor.indenter import Indenter
 from Orange.widgets.data.utils.pythoneditor.lines import Lines
 from Orange.widgets.data.utils.pythoneditor.rectangularselection import RectangularSelection
-from Orange.widgets.data.utils.pythoneditor.vim import Vim, isChar
+from Orange.widgets.data.utils.pythoneditor.vim import Vim, isChar, code, key_code
 
 
 # pylint: disable=protected-access
@@ -952,7 +952,7 @@ def typeOverwrite(text):
             # make action shortcuts override keyboard events (non-default Qt behaviour)
             for action in self.actions():
                 seq = action.shortcut()
-                if seq.count() == 1 and seq[0] == event.key() | int(event.modifiers()):
+                if seq.count() == 1 and key_code(seq[0]) == code(event):
                     action.trigger()
                     break
             else:
@@ -1023,7 +1023,7 @@ def showEvent(self, ev):
     def _updateTabStopWidth(self):
         """Update tabstop width after font or indentation changed
         """
-        self.setTabStopWidth(self.fontMetrics().horizontalAdvance(' ' * self._indenter.width))
+        self.setTabStopDistance(self.fontMetrics().horizontalAdvance(' ' * self._indenter.width))
 
     @property
     def lines(self):
diff --git a/Orange/widgets/data/utils/pythoneditor/indenter.py b/Orange/widgets/data/utils/pythoneditor/indenter.py
index 6ec237e3ef1..bf2fd326130 100644
--- a/Orange/widgets/data/utils/pythoneditor/indenter.py
+++ b/Orange/widgets/data/utils/pythoneditor/indenter.py
@@ -7,7 +7,7 @@
 as published by the Free Software Foundation, version 2.1 of the license.
 This is compatible with Orange3's GPL-3.0 license.
 """
-from PyQt5.QtGui import QTextCursor
+from AnyQt.QtGui import QTextCursor
 
 # pylint: disable=pointless-string-statement
 
diff --git a/Orange/widgets/data/utils/pythoneditor/lines.py b/Orange/widgets/data/utils/pythoneditor/lines.py
index 8e7d31cf887..bed65ec6bd2 100644
--- a/Orange/widgets/data/utils/pythoneditor/lines.py
+++ b/Orange/widgets/data/utils/pythoneditor/lines.py
@@ -7,7 +7,7 @@
 as published by the Free Software Foundation, version 2.1 of the license.
 This is compatible with Orange3's GPL-3.0 license.
 """
-from PyQt5.QtGui import QTextCursor
+from AnyQt.QtGui import QTextCursor
 
 # Lines class.
 # list-like object for access text document lines
diff --git a/Orange/widgets/data/utils/pythoneditor/rectangularselection.py b/Orange/widgets/data/utils/pythoneditor/rectangularselection.py
index 8dcc70eff54..1977649e55e 100644
--- a/Orange/widgets/data/utils/pythoneditor/rectangularselection.py
+++ b/Orange/widgets/data/utils/pythoneditor/rectangularselection.py
@@ -7,9 +7,9 @@
 as published by the Free Software Foundation, version 2.1 of the license.
 This is compatible with Orange3's GPL-3.0 license.
 """
-from PyQt5.QtCore import Qt, QMimeData
-from PyQt5.QtWidgets import QApplication, QTextEdit
-from PyQt5.QtGui import QKeyEvent, QKeySequence, QPalette, QTextCursor
+from AnyQt.QtCore import Qt, QMimeData
+from AnyQt.QtWidgets import QApplication, QTextEdit
+from AnyQt.QtGui import QKeyEvent, QKeySequence, QPalette, QTextCursor
 
 
 class RectangularSelection:
@@ -71,7 +71,7 @@ def onExpandKeyEvent(self, keyEvent):
                                                       self._qpart.cursorPosition[1])
             self._start = (line, visibleColumn)
         modifiersWithoutAltShift = keyEvent.modifiers() & (~(Qt.AltModifier | Qt.ShiftModifier))
-        newEvent = QKeyEvent(keyEvent.type(),
+        newEvent = QKeyEvent(QKeyEvent.Type(keyEvent.type()),
                              keyEvent.key(),
                              modifiersWithoutAltShift,
                              keyEvent.text(),
diff --git a/Orange/widgets/data/utils/pythoneditor/tests/base.py b/Orange/widgets/data/utils/pythoneditor/tests/base.py
index 1fd3d4aaec5..704678f7b81 100644
--- a/Orange/widgets/data/utils/pythoneditor/tests/base.py
+++ b/Orange/widgets/data/utils/pythoneditor/tests/base.py
@@ -14,8 +14,11 @@
 from AnyQt.QtTest import QTest
 from AnyQt.QtCore import Qt, QCoreApplication
 
+from orangewidget.utils import enum_as_int
+
 from Orange.widgets import widget
 from Orange.widgets.data.utils.pythoneditor.editor import PythonEditor
+from Orange.widgets.data.utils.pythoneditor.vim import key_code
 
 
 def _processPendingEvents(app):
@@ -23,7 +26,7 @@ def _processPendingEvents(app):
     Timeout is used, because on Windows hasPendingEvents() always returns True
     """
     t = time.time()
-    while app.hasPendingEvents() and (time.time() - t < 0.1):
+    while time.time() - t < 0.1:
         app.processEvents()
 
 
@@ -68,12 +71,12 @@ def keySequenceClicks(widget_, keySequence, extraModifiers=Qt.NoModifier):
     # pylint: disable=line-too-long
     # This is based on a simplified version of http://stackoverflow.com/questions/14034209/convert-string-representation-of-keycode-to-qtkey-or-any-int-and-back. I added code to handle the case in which the resulting key contains a modifier (for example, Shift+Home). When I execute QTest.keyClick(widget, keyWithModifier), I get the error "ASSERT: "false" in file .\qasciikey.cpp, line 495". To fix this, the following code splits the key into a key and its modifier.
     # Bitmask for all modifier keys.
-    modifierMask = int(Qt.ShiftModifier | Qt.ControlModifier | Qt.AltModifier |
-                       Qt.MetaModifier |  Qt.KeypadModifier)
+    modifierMask = enum_as_int(Qt.KeyboardModifierMask)
     ks = QKeySequence(keySequence)
     # For now, we don't handle a QKeySequence("Ctrl") or any other modified by itself.
     assert ks.count() > 0
     for _, key in enumerate(ks):
-        modifiers = Qt.KeyboardModifiers((key & modifierMask) | extraModifiers)
+        key = key_code(key)
+        modifiers = Qt.KeyboardModifiers((key & modifierMask) | enum_as_int(extraModifiers))
         key = key & ~modifierMask
-        QTest.keyClick(widget_, key, modifiers, 10)
+        QTest.keyClick(widget_, Qt.Key(key), modifiers, 10)
diff --git a/Orange/widgets/data/utils/pythoneditor/vim.py b/Orange/widgets/data/utils/pythoneditor/vim.py
index 65d45579c44..a14da7b50cb 100644
--- a/Orange/widgets/data/utils/pythoneditor/vim.py
+++ b/Orange/widgets/data/utils/pythoneditor/vim.py
@@ -9,9 +9,11 @@
 """
 import sys
 
-from PyQt5.QtCore import Qt, pyqtSignal, QObject
-from PyQt5.QtWidgets import QTextEdit
-from PyQt5.QtGui import QColor, QTextCursor
+from AnyQt.QtCore import Qt, pyqtSignal, QObject
+from AnyQt.QtWidgets import QTextEdit
+from AnyQt.QtGui import QColor, QTextCursor
+
+from orangewidget.utils import enum_as_int
 
 # pylint: disable=protected-access
 # pylint: disable=unused-argument
@@ -24,38 +26,46 @@
 for charCode in range(ord('a'), ord('z') + 1):
     shortName = chr(charCode)
     longName = 'Key_' + shortName.upper()
-    qtCode = getattr(Qt, longName)
+    qtCode = enum_as_int(getattr(Qt, longName))
     setattr(thismodule, '_' + shortName, qtCode)
-    setattr(thismodule, '_' + shortName.upper(), Qt.ShiftModifier + qtCode)
-
-_0 = Qt.Key_0
-_Dollar = Qt.ShiftModifier + Qt.Key_Dollar
-_Percent = Qt.ShiftModifier + Qt.Key_Percent
-_Caret = Qt.ShiftModifier + Qt.Key_AsciiCircum
-_Esc = Qt.Key_Escape
-_Insert = Qt.Key_Insert
-_Down = Qt.Key_Down
-_Up = Qt.Key_Up
-_Left = Qt.Key_Left
-_Right = Qt.Key_Right
-_Space = Qt.Key_Space
-_BackSpace = Qt.Key_Backspace
-_Equal = Qt.Key_Equal
-_Less = Qt.ShiftModifier + Qt.Key_Less
-_Greater = Qt.ShiftModifier + Qt.Key_Greater
-_Home = Qt.Key_Home
-_End = Qt.Key_End
-_PageDown = Qt.Key_PageDown
-_PageUp = Qt.Key_PageUp
-_Period = Qt.Key_Period
-_Enter = Qt.Key_Enter
-_Return = Qt.Key_Return
+    setattr(thismodule, '_' + shortName.upper(), enum_as_int(Qt.ShiftModifier) | qtCode)
+
+
+def key_code(comb):
+    try:
+        return comb.toCombined()
+    except AttributeError:
+        return enum_as_int(comb)
+
+
+_0 = key_code(Qt.Key_0)
+_Dollar = key_code(Qt.ShiftModifier | Qt.Key_Dollar)
+_Percent = key_code(Qt.ShiftModifier | Qt.Key_Percent)
+_Caret = key_code(Qt.ShiftModifier | Qt.Key_AsciiCircum)
+_Esc = key_code(Qt.Key_Escape)
+_Insert = key_code(Qt.Key_Insert)
+_Down = key_code(Qt.Key_Down)
+_Up = key_code(Qt.Key_Up)
+_Left = key_code(Qt.Key_Left)
+_Right = key_code(Qt.Key_Right)
+_Space = key_code(Qt.Key_Space)
+_BackSpace = key_code(Qt.Key_Backspace)
+_Equal = key_code(Qt.Key_Equal)
+_Less = key_code(Qt.ShiftModifier | Qt.Key_Less)
+_Greater = key_code(Qt.ShiftModifier | Qt.Key_Greater)
+_Home = key_code(Qt.Key_Home)
+_End = key_code(Qt.Key_End)
+_PageDown = key_code(Qt.Key_PageDown)
+_PageUp = key_code(Qt.Key_PageUp)
+_Period = key_code(Qt.Key_Period)
+_Enter = key_code(Qt.Key_Enter)
+_Return = key_code(Qt.Key_Return)
 
 
 def code(ev):
     modifiers = ev.modifiers()
     modifiers &= ~Qt.KeypadModifier  # ignore keypad modifier to handle both main and numpad numbers
-    return int(modifiers) + ev.key()
+    return enum_as_int(modifiers) | ev.key()
 
 
 def isChar(ev):
diff --git a/Orange/widgets/evaluate/tests/test_owcalibrationplot.py b/Orange/widgets/evaluate/tests/test_owcalibrationplot.py
index 9819e455b4c..a3aed51098f 100644
--- a/Orange/widgets/evaluate/tests/test_owcalibrationplot.py
+++ b/Orange/widgets/evaluate/tests/test_owcalibrationplot.py
@@ -9,12 +9,13 @@
 
 from sklearn.exceptions import ConvergenceWarning
 
+from orangewidget.utils.combobox import qcombobox_emit_activated
+
 from Orange.data import Table, DiscreteVariable, Domain, ContinuousVariable
 import Orange.evaluation
 import Orange.classification
 from Orange.evaluation import Results
 from Orange.evaluation.performance_curves import Curves
-
 from Orange.widgets.evaluate.tests.base import EvaluateTest
 from Orange.widgets.evaluate.owcalibrationplot import OWCalibrationPlot
 from Orange.widgets.tests.base import WidgetTest
@@ -141,8 +142,7 @@ def test_regression_input_error(self):
     @staticmethod
     def _set_combo(combo, val):
         combo.setCurrentIndex(val)
-        combo.activated[int].emit(val)
-        combo.activated[str].emit(combo.currentText())
+        qcombobox_emit_activated(combo, val)
 
     @staticmethod
     def _set_radio_buttons(radios, val):
diff --git a/Orange/widgets/gui.py b/Orange/widgets/gui.py
index 59052f914bf..5df440a391f 100644
--- a/Orange/widgets/gui.py
+++ b/Orange/widgets/gui.py
@@ -650,7 +650,8 @@ def __init__(self, *args, **kwargs):
         self.horizontalScrollBar().setSingleStep(20)
 
     def wheelEvent(self, event: QWheelEvent):
-        if event.source() == Qt.MouseEventNotSynthesized and \
+        if hasattr(event, "source") and \
+                event.source() == Qt.MouseEventNotSynthesized and \
                 (event.modifiers() & Qt.ShiftModifier and sys.platform == 'darwin' or
                  event.modifiers() & Qt.AltModifier and sys.platform != 'darwin'):
             new_event = QWheelEvent(
diff --git a/Orange/widgets/model/tests/test_owrandomforest.py b/Orange/widgets/model/tests/test_owrandomforest.py
index 32d10e98dfe..c360f06a9f6 100644
--- a/Orange/widgets/model/tests/test_owrandomforest.py
+++ b/Orange/widgets/model/tests/test_owrandomforest.py
@@ -1,5 +1,6 @@
 # Test methods with long descriptive names can omit docstrings
 # pylint: disable=missing-docstring
+from AnyQt.QtCore import Qt
 from Orange.data import Table
 from Orange.widgets.model.owrandomforest import OWRandomForest
 from Orange.widgets.tests.base import (
@@ -26,8 +27,8 @@ def test_parameters_checked(self):
         """Check learner and model for various values of all parameters
         when all properties are checked
         """
-        self.widget.max_features_spin[0].setCheckState(True)
-        self.widget.max_depth_spin[0].setCheckState(True)
+        self.widget.max_features_spin[0].setCheckState(Qt.Checked)
+        self.widget.max_depth_spin[0].setCheckState(Qt.Checked)
         self.parameters.extend([
             ParameterMapping("max_features", self.widget.max_features_spin[1]),
             ParameterMapping("max_depth", self.widget.max_depth_spin[1])])
@@ -37,7 +38,7 @@ def test_parameters_unchecked(self):
         """Check learner and model for various values of all parameters
         when properties are not checked
         """
-        self.widget.min_samples_split_spin[0].setCheckState(False)
+        self.widget.min_samples_split_spin[0].setCheckState(Qt.Unchecked)
         self.parameters = self.parameters[:1]
         self.parameters.extend([
             DefaultParameterMapping("max_features", "auto"),
diff --git a/Orange/widgets/model/tests/test_owsvm.py b/Orange/widgets/model/tests/test_owsvm.py
index af84ec49351..38f231f85a6 100644
--- a/Orange/widgets/model/tests/test_owsvm.py
+++ b/Orange/widgets/model/tests/test_owsvm.py
@@ -2,6 +2,7 @@
 # pylint: disable=missing-docstring
 from scipy.sparse import csr_matrix
 
+from AnyQt.QtCore import Qt
 from Orange.widgets.model.owsvm import OWSVM
 from Orange.widgets.tests.base import (
     WidgetTest,
@@ -47,7 +48,7 @@ def test_parameters_unchecked(self):
         """Check learner and model for various values of all parameters
         when Iteration limit is not checked
         """
-        self.widget.max_iter_spin[0].setCheckState(False)
+        self.widget.max_iter_spin[0].setCheckState(Qt.Unchecked)
         self.parameters[-1] = DefaultParameterMapping("max_iter", -1)
         self.test_parameters()
 
diff --git a/Orange/widgets/model/tests/test_tree.py b/Orange/widgets/model/tests/test_tree.py
index 2f3d919d39b..d9702e7578b 100644
--- a/Orange/widgets/model/tests/test_tree.py
+++ b/Orange/widgets/model/tests/test_tree.py
@@ -1,5 +1,6 @@
 # pylint: disable=protected-access
 import numpy as np
+from AnyQt.QtCore import Qt
 
 from Orange.base import Model
 from Orange.data import Table
@@ -35,7 +36,7 @@ def test_parameters_unchecked(self):
         when pruning parameters are not checked
         """
         for cb in self.checks:
-            cb.setCheckState(False)
+            cb.setCheckState(Qt.Unchecked)
         self.parameters = [DefaultParameterMapping(par.name, val)
                            for par, val in zip(self.parameters, (None, 2, 1))]
         self.test_parameters()
diff --git a/Orange/widgets/tests/base.py b/Orange/widgets/tests/base.py
index 5c6016f5469..6960172a9e4 100644
--- a/Orange/widgets/tests/base.py
+++ b/Orange/widgets/tests/base.py
@@ -7,8 +7,8 @@
 import numpy as np
 import scipy.sparse as sp
 
+from AnyQt.QtCore import Qt, QRectF, QPointF
 from AnyQt.QtGui import QFont, QTextDocumentFragment
-from AnyQt.QtCore import QRectF, QPointF
 from AnyQt.QtTest import QSignalSpy
 from AnyQt.QtWidgets import (
     QComboBox, QSpinBox, QDoubleSpinBox, QSlider
@@ -691,7 +691,8 @@ def test_class_density(self, timeout=DEFAULT_TIMEOUT):
 
     def test_dragging_tooltip(self):
         """Dragging tooltip depends on data being jittered"""
-        text = QTextDocumentFragment.fromHtml(self.widget.graph.tiptexts[0]).toPlainText()
+        text = QTextDocumentFragment.fromHtml(
+            self.widget.graph.tiptexts[Qt.NoModifier]).toPlainText()
         self.send_signal(self.widget.Inputs.data, Table("heart_disease"))
         self.assertEqual(self.widget.graph.tip_textitem.toPlainText(), text)
 
diff --git a/Orange/widgets/tests/utils.py b/Orange/widgets/tests/utils.py
index 91ad53b9d66..51a0d816b74 100644
--- a/Orange/widgets/tests/utils.py
+++ b/Orange/widgets/tests/utils.py
@@ -1,305 +1,21 @@
-import sys
 from functools import wraps
 
-import warnings
-import contextlib
+from AnyQt.QtCore import Qt, QLocale, QPoint, QT_VERSION_INFO
+from AnyQt.QtTest import QTest
+from AnyQt.QtGui import QContextMenuEvent
+from AnyQt.QtWidgets import QApplication, QWidget, QButtonGroup
 
-from AnyQt.QtCore import (
-    Qt, QObject, QEventLoop, QTimer, QLocale, QPoint, QT_VERSION_INFO
+from orangewidget.tests.utils import (
+    simulate, excepthook_catch, EventSpy, mouseMove
 )
-from AnyQt.QtTest import QTest
-from AnyQt.QtGui import QMouseEvent, QContextMenuEvent
-from AnyQt.QtWidgets import QApplication, QWidget, QButtonGroup, QComboBox
 
 from Orange.data import Table, Domain, ContinuousVariable
 
-
-class EventSpy(QObject):
-    """
-    A testing utility class (similar to QSignalSpy) to record events
-    delivered to a QObject instance.
-
-    Note
-    ----
-    Only event types can be recorded (as QEvent instances are deleted
-    on delivery).
-
-    Note
-    ----
-    Can only be used with a QCoreApplication running.
-
-    Parameters
-    ----------
-    object : QObject
-        An object whose events need to be recorded.
-    etype : Union[QEvent.Type, Sequence[QEvent.Type]
-        A event type (or types) that should be recorded
-    """
-    def __init__(self, object, etype, **kwargs):
-        super().__init__(**kwargs)
-        if not isinstance(object, QObject):
-            raise TypeError
-
-        self.__object = object
-        try:
-            len(etype)
-        except TypeError:
-            etypes = {etype}
-        else:
-            etypes = set(etype)
-
-        self.__etypes = etypes
-        self.__record = []
-        self.__loop = QEventLoop()
-        self.__timer = QTimer(self, singleShot=True)
-        self.__timer.timeout.connect(self.__loop.quit)
-        self.__object.installEventFilter(self)
-
-    def wait(self, timeout=5000):
-        """
-        Start an event loop that runs until a spied event or a timeout occurred.
-
-        Parameters
-        ----------
-        timeout : int
-            Timeout in milliseconds.
-
-        Returns
-        -------
-        res : bool
-            True if the event occurred and False otherwise.
-
-        Example
-        -------
-        >>> app = QCoreApplication.instance() or QCoreApplication([])
-        >>> obj = QObject()
-        >>> spy = EventSpy(obj, QEvent.User)
-        >>> app.postEvent(obj, QEvent(QEvent.User))
-        >>> spy.wait()
-        True
-        >>> print(spy.events())
-        [1000]
-        """
-        count = len(self.__record)
-        self.__timer.stop()
-        self.__timer.setInterval(timeout)
-        self.__timer.start()
-        self.__loop.exec()
-        self.__timer.stop()
-        return len(self.__record) != count
-
-    def eventFilter(self, reciever, event):
-        if reciever is self.__object and event.type() in self.__etypes:
-            self.__record.append(event.type())
-            if self.__loop.isRunning():
-                self.__loop.quit()
-        return super().eventFilter(reciever, event)
-
-    def events(self):
-        """
-        Return a list of all (listened to) event types that occurred.
-
-        Returns
-        -------
-        events : List[QEvent.Type]
-        """
-        return list(self.__record)
-
-
-@contextlib.contextmanager
-def excepthook_catch(raise_on_exit=True):
-    """
-    Override `sys.excepthook` with a custom handler to record unhandled
-    exceptions.
-
-    Use this to capture or note exceptions that are raised and
-    unhandled within PyQt slots or virtual function overrides.
-
-    Note
-    ----
-    The exceptions are still dispatched to the original `sys.excepthook`
-
-    Parameters
-    ----------
-    raise_on_exit : bool
-        If True then the (first) exception that was captured will be
-        reraised on context exit
-
-    Returns
-    -------
-    ctx : ContextManager
-        A context manager
-
-    Example
-    -------
-    >>> class Obj(QObject):
-    ...     signal = pyqtSignal()
-    ...
-    >>> o = Obj()
-    >>> o.signal.connect(lambda : 1/0)
-    >>> with excepthook_catch(raise_on_exit=False) as exc_list:
-    ...    o.signal.emit()
-    ...
-    >>> print(exc_list)  # doctest: +ELLIPSIS
-    [(<class 'ZeroDivisionError'>, ZeroDivisionError('division by zero',), ...
-    """
-    excepthook = sys.excepthook
-    seen = []
-
-    def excepthook_handle(exctype, value, traceback):
-        seen.append((exctype, value, traceback))
-        excepthook(exctype, value, traceback)
-
-    sys.excepthook = excepthook_handle
-    shouldraise = raise_on_exit
-    try:
-        yield seen
-    except BaseException:
-        # propagate/preserve exceptions from within the ctx
-        shouldraise = False
-        raise
-    finally:
-        if sys.excepthook == excepthook_handle:
-            sys.excepthook = excepthook
-        else:
-            raise RuntimeError(
-                "The sys.excepthook that was installed by "
-                "'excepthook_catch' context at enter is not "
-                "the one present at exit.")
-        if shouldraise and seen:
-            raise seen[0][1]
-
-
-class simulate:
-    """
-    Utility functions for simulating user interactions with Qt widgets.
-    """
-    @staticmethod
-    def combobox_run_through_all(cbox, delay=-1, callback=None):
-        """
-        Run through all items in a given combo box, simulating the user
-        focusing the combo box and pressing the Down arrow key activating
-        all the items on the way.
-
-        Unhandled exceptions from invoked PyQt slots/virtual function overrides
-        are captured and reraised.
-
-        Parameters
-        ----------
-        cbox : QComboBox
-        delay : int
-            Run the event loop after the simulated key press (-1, the default,
-            means no delay)
-        callback : callable
-            A callback that will be executed after every item change. Takes no
-            parameters.
-
-        See Also
-        --------
-        QTest.keyClick
-        """
-        assert cbox.focusPolicy() & Qt.TabFocus
-        cbox.setFocus(Qt.TabFocusReason)
-        cbox.setCurrentIndex(-1)
-        for i in range(cbox.count()):
-            with excepthook_catch() as exlist:
-                QTest.keyClick(cbox, Qt.Key_Down, delay=delay)
-                if callback:
-                    callback()
-            if exlist:
-                raise exlist[0][1] from exlist[0][1]
-
-    @staticmethod
-    def combobox_activate_index(cbox, index, delay=-1):
-        """
-        Activate an item at `index` in a given combo box.
-
-        The item at index **must** be enabled and selectable.
-
-        Parameters
-        ----------
-        cbox : QComboBox
-        index : int
-        delay : int
-            Run the event loop after the signals are emitted for `delay`
-            milliseconds (-1, the default, means no delay).
-        """
-        assert 0 <= index < cbox.count()
-        model = cbox.model()
-        column = cbox.modelColumn()
-        root = cbox.rootModelIndex()
-        mindex = model.index(index, column, root)
-        assert mindex.flags() & Qt.ItemIsEnabled
-        cbox.setCurrentIndex(index)
-        # QComboBox does not have an interface which would allow selecting
-        # the current item as if a user would. Only setCurrentIndex which
-        # does not emit the activated signals.
-        qcombobox_emit_activated(cbox, index)
-        if delay >= 0:
-            QTest.qWait(delay)
-
-    @staticmethod
-    def combobox_index_of(cbox, value, role=Qt.DisplayRole):
-        """
-        Find the index of an **selectable** item in a combo box whose `role`
-        data contains the given `value`.
-
-        Parameters
-        ----------
-        cbox : QComboBox
-        value : Any
-        role : Qt.ItemDataRole
-
-        Returns
-        -------
-        index : int
-            An index such that `cbox.itemData(index, role) == value` **and**
-            the item is enabled for selection or -1 if such an index could
-            not be found.
-        """
-        model = cbox.model()
-        column = cbox.modelColumn()
-        root = cbox.rootModelIndex()
-        for i in range(model.rowCount(root)):
-            index = model.index(i, column, root)
-            if index.data(role) == value and \
-                    index.flags() & Qt.ItemIsEnabled:
-                pos = i
-                break
-        else:
-            pos = -1
-        return pos
-
-    @staticmethod
-    def combobox_activate_item(cbox, value, role=Qt.DisplayRole, delay=-1):
-        """
-        Find an **selectable** item in a combo box whose `role` data
-        contains the given value and activate it.
-
-        Raise an ValueError if the item could not be found.
-
-        Parameters
-        ----------
-        cbox : QComboBox
-        value : Any
-        role : Qt.ItemDataRole
-        delay : int
-            Run the event loop after the signals are emitted for `delay`
-            milliseconds (-1, the default, means no delay).
-        """
-        index = simulate.combobox_index_of(cbox, value, role)
-        if index < 0:
-            raise ValueError("{!r} not in {}".format(value, cbox))
-        simulate.combobox_activate_index(cbox, index, delay)
-
-
-def qcombobox_emit_activated(cb: QComboBox, index: int):
-    cb.activated[int].emit(index)
-    text = cb.itemText(index)
-    if QT_VERSION_INFO >= (5, 15):
-        cb.textActivated.emit(text)
-    if QT_VERSION_INFO < (6, 0):
-        cb.activated[str].emit(text)
+# pylint: disable=self-assigning-variable,invalid-name
+EventSpy = EventSpy
+excepthook_catch = excepthook_catch
+simulate = simulate
+mouseMove = mouseMove
 
 
 def qbuttongroup_emit_clicked(bg: QButtonGroup, id_: int):
@@ -324,18 +40,6 @@ def wrap(*args, **kwargs):
     return wrapper
 
 
-def mouseMove(widget, pos=QPoint(), delay=-1):  # pragma: no-cover
-    # Like QTest.mouseMove, but functional without QCursor.setPos
-    if pos.isNull():
-        pos = widget.rect().center()
-    me = QMouseEvent(QMouseEvent.MouseMove, pos, widget.mapToGlobal(pos),
-                     Qt.NoButton, Qt.MouseButtons(0), Qt.NoModifier)
-    if delay > 0:
-        QTest.qWait(delay)
-
-    QApplication.sendEvent(widget, me)
-
-
 def contextMenu(
         widget: QWidget, pos=QPoint(), reason=QContextMenuEvent.Mouse,
         modifiers=Qt.NoModifier, delay=-1
diff --git a/Orange/widgets/unsupervised/owdistancematrix.py b/Orange/widgets/unsupervised/owdistancematrix.py
index c043b0d52e1..900e9e77299 100644
--- a/Orange/widgets/unsupervised/owdistancematrix.py
+++ b/Orange/widgets/unsupervised/owdistancematrix.py
@@ -86,12 +86,12 @@ def data(self, index, role=Qt.DisplayRole):
         if role == FixedFormatNumericColumnDelegate.ColumnDataSpanRole:
             return 0., self.span
         if row == col and self.zero_diag:
-            if role == Qt.BackgroundColorRole and self.variable:
+            if role == Qt.BackgroundRole and self.variable:
                 return self.color_for_label(row, 200)
             return
         if role == Qt.DisplayRole:
             return float(self.distances[row, col])
-        if role == Qt.BackgroundColorRole:
+        if role == Qt.BackgroundRole:
             return self.color_for_cell(row, col)
         if role == Qt.ForegroundRole:
             return QColor(Qt.black)  # the background is light-ish
diff --git a/Orange/widgets/utils/colorpalette.py b/Orange/widgets/utils/colorpalette.py
index a08472d8c7d..e595f86fed0 100644
--- a/Orange/widgets/utils/colorpalette.py
+++ b/Orange/widgets/utils/colorpalette.py
@@ -915,7 +915,7 @@ def __init__(self, master=None, parent=None, label=None, color=None):
     def setColor(self, color):
         self.color = color
         palette = QPalette()
-        palette.setBrush(QPalette.Background, color)
+        palette.setBrush(QPalette.Window, color)
         self.icon.setPalette(palette)
 
     def getColor(self):
diff --git a/Orange/widgets/utils/dendrogram.py b/Orange/widgets/utils/dendrogram.py
index d7ddca99142..6624d099124 100644
--- a/Orange/widgets/utils/dendrogram.py
+++ b/Orange/widgets/utils/dendrogram.py
@@ -347,7 +347,7 @@ def setRoot(self, root):
         self.clear()
         self._root = root
         if root is not None:
-            foreground = self.palette().color(QPalette.Foreground)
+            foreground = self.palette().color(QPalette.WindowText)
             pen = make_pen(foreground, width=1, cosmetic=True,
                            join_style=Qt.MiterJoin)
             for node in postorder(root):
@@ -445,7 +445,7 @@ def branches(item):
 
         if self._highlighted_item:
             # Restore the previous item
-            highlight = self.palette().color(QPalette.Foreground)
+            highlight = self.palette().color(QPalette.WindowText)
             set_pen(self._highlighted_item,
                     make_pen(highlight, width=1, cosmetic=True))
 
@@ -856,7 +856,7 @@ def branches(item):
             for it in postorder(item, branches):
                 it.setPen(update_pen(it.pen(), brush=color))
         if self._root is not None:
-            foreground = self.palette().color(QPalette.Foreground)
+            foreground = self.palette().color(QPalette.WindowText)
             item = self.item(self._root)
             set_color(item, foreground)
         highlight = self.palette().color(QPalette.Highlight)
diff --git a/Orange/widgets/utils/domaineditor.py b/Orange/widgets/utils/domaineditor.py
index d9f9b016540..7be5c5014c5 100644
--- a/Orange/widgets/utils/domaineditor.py
+++ b/Orange/widgets/utils/domaineditor.py
@@ -161,7 +161,7 @@ def hidePopup(me):
                 self.view.closeEditor(me, self.NoHint)
 
         combo = Combo(parent)
-        combo.highlighted[str].connect(combo.highlight)
+        combo.textHighlighted.connect(combo.highlight)
         return combo
 
 
diff --git a/Orange/widgets/utils/graphicspixmapwidget.py b/Orange/widgets/utils/graphicspixmapwidget.py
index aff86b77852..09934b97845 100644
--- a/Orange/widgets/utils/graphicspixmapwidget.py
+++ b/Orange/widgets/utils/graphicspixmapwidget.py
@@ -112,7 +112,9 @@ def paint(
         exposedcrect = crect.intersected(exposed)
         pixmaptransform = self.pixmapTransform()
         # map exposed rect to exposed pixmap coords
-        assert pixmaptransform.type() <= QTransform.TxRotate
+        assert pixmaptransform.type() in (
+            QTransform.TxNone, QTransform.TxTranslate, QTransform.TxScale
+        )
         pixmaptransform, ok = pixmaptransform.inverted()
         if not ok:
             painter.drawPixmap(
diff --git a/Orange/widgets/utils/graphicsview.py b/Orange/widgets/utils/graphicsview.py
index 01c41b898a5..93e7805c6a5 100644
--- a/Orange/widgets/utils/graphicsview.py
+++ b/Orange/widgets/utils/graphicsview.py
@@ -9,6 +9,8 @@
 from AnyQt.QtCore import (
     pyqtSignal as Signal, pyqtProperty as Property, pyqtSlot as Slot
 )
+from orangecanvas.utils import qsizepolicy_is_expanding, \
+    qsizepolicy_is_shrinking
 
 from Orange.widgets.utils.graphicslayoutitem import scaled
 
@@ -282,9 +284,10 @@ def adjusted_size(
     elif policy == QSizePolicy.Ignored:
         return min(max(available, minimum), maximum)
     size = hint
-    if policy & QSizePolicy.ExpandFlag and hint < available:
+
+    if qsizepolicy_is_expanding(policy) and hint < available:
         size = min(max(size, available), maximum)
-    if policy & QSizePolicy.ShrinkFlag and hint > available:
+    if qsizepolicy_is_shrinking(policy) and hint > available:
         size = max(min(size, available), minimum)
     return size
 
diff --git a/Orange/widgets/utils/headerview.py b/Orange/widgets/utils/headerview.py
index 75fc474ab70..41f9782e2b2 100644
--- a/Orange/widgets/utils/headerview.py
+++ b/Orange/widgets/utils/headerview.py
@@ -107,8 +107,8 @@ def initStyleOptionForIndex(
                          else defaultAlignment)
 
         option.section = logicalIndex
-        option.state = QStyle.State(int(option.state) | int(state))
-        option.textAlignment = Qt.Alignment(int(textAlignment))
+        option.state = QStyle.State(option.state | state)
+        option.textAlignment = Qt.Alignment(textAlignment)
 
         option.iconAlignment = Qt.AlignVCenter
         text = model.headerData(logicalIndex, self.orientation(),
diff --git a/Orange/widgets/utils/stickygraphicsview.py b/Orange/widgets/utils/stickygraphicsview.py
index dee2a042958..d228c0f5edb 100644
--- a/Orange/widgets/utils/stickygraphicsview.py
+++ b/Orange/widgets/utils/stickygraphicsview.py
@@ -24,7 +24,7 @@ def __init__(self, *args, **kwargs) -> None:
         ds = QGraphicsDropShadowEffect(
             parent=self,
             objectName="sticky-view-shadow",
-            color=palette.color(QPalette.Foreground),
+            color=palette.color(QPalette.WindowText),
             blurRadius=15,
             offset=QPointF(0, 0),
             enabled=True
@@ -38,7 +38,7 @@ def changeEvent(self, event: QEvent) -> None:
                 QGraphicsDropShadowEffect, "sticky-view-shadow")
             if effect is not None:
                 palette = self.palette()
-                effect.setColor(palette.color(QPalette.Foreground))
+                effect.setColor(palette.color(QPalette.WindowText))
 
     def eventFilter(self, recv: QObject, event: QEvent) -> bool:
         if event.type() in (QEvent.Show, QEvent.Hide) and recv is self.widget():
@@ -151,8 +151,10 @@ def setupViewport(self, widget: QWidget) -> None:
             sizePolicy=sp,
             visible=False,
         )
-        over.setLayout(QVBoxLayout(margin=0))
-        over.layout().addWidget(header)
+        layout = QVBoxLayout()
+        layout.setContentsMargins(0, 0, 0, 0)
+        layout.addWidget(header)
+        over.setLayout(layout)
         over.setWidget(widget)
 
         over = _OverlayWidget(
@@ -161,8 +163,10 @@ def setupViewport(self, widget: QWidget) -> None:
             sizePolicy=sp,
             visible=False
         )
-        over.setLayout(QVBoxLayout(margin=0))
-        over.layout().addWidget(footer)
+        layout = QVBoxLayout()
+        layout.setContentsMargins(0, 0, 0, 0)
+        layout.addWidget(footer)
+        over.setLayout(layout)
         over.setWidget(widget)
 
         def bind(source: QScrollBar, target: QScrollBar) -> None:
diff --git a/Orange/widgets/utils/tests/test_graphicspixmapwidget.py b/Orange/widgets/utils/tests/test_graphicspixmapwidget.py
new file mode 100644
index 00000000000..dd9d8721556
--- /dev/null
+++ b/Orange/widgets/utils/tests/test_graphicspixmapwidget.py
@@ -0,0 +1,37 @@
+from AnyQt.QtCore import Qt, QSize, QSizeF
+from AnyQt.QtGui import QPixmap
+from AnyQt.QtWidgets import QGraphicsScene, QGraphicsView
+
+from orangewidget.tests.base import GuiTest
+from Orange.widgets.utils.graphicspixmapwidget import GraphicsPixmapWidget
+
+
+class TestGraphicsPixmapWidget(GuiTest):
+    def setUp(self) -> None:
+        super().setUp()
+        self.scene = QGraphicsScene()
+        self.view = QGraphicsView(self.scene)
+
+    def tearDown(self) -> None:
+        self.scene.clear()
+        self.scene.deleteLater()
+        self.view.deleteLater()
+        del self.scene
+        del self.view
+
+    def test_graphicspixmapwidget(self):
+        w = GraphicsPixmapWidget()
+        self.scene.addItem(w)
+        w.setPixmap(QPixmap(100, 100))
+        p = w.pixmap()
+        self.assertEqual(p.size(), QSize(100, 100))
+        self.view.grab()
+        w.setScaleContents(True)
+        w.setAspectRatioMode(Qt.KeepAspectRatio)
+        s = w.sizeHint(Qt.PreferredSize)
+        self.assertEqual(s, QSizeF(100., 100.))
+        s = w.sizeHint(Qt.PreferredSize, QSizeF(200., -1.))
+        self.assertEqual(s, QSizeF(200., 200.))
+        s = w.sizeHint(Qt.PreferredSize, QSizeF(-1., 200.))
+        self.assertEqual(s, QSizeF(200., 200.))
+        self.view.grab()
diff --git a/Orange/widgets/utils/tests/test_itemmodels.py b/Orange/widgets/utils/tests/test_itemmodels.py
index cdc8806b5d2..a377d2b3bde 100644
--- a/Orange/widgets/utils/tests/test_itemmodels.py
+++ b/Orange/widgets/utils/tests/test_itemmodels.py
@@ -62,8 +62,8 @@ def test_data(self):
 
     def test_editable(self):
         editable_model = PyTableModel([[0]], editable=True)
-        self.assertFalse(int(self.model.flags(self.model.index(0, 0)) & Qt.ItemIsEditable))
-        self.assertTrue(int(editable_model.flags(editable_model.index(0, 0)) & Qt.ItemIsEditable))
+        self.assertFalse(bool(self.model.flags(self.model.index(0, 0)) & Qt.ItemIsEditable))
+        self.assertTrue(bool(editable_model.flags(editable_model.index(0, 0)) & Qt.ItemIsEditable))
 
     def test_sort(self):
         self.model.sort(1)
diff --git a/Orange/widgets/utils/tests/test_stickygraphicsview.py b/Orange/widgets/utils/tests/test_stickygraphicsview.py
index 9d5f1b468ea..db2cbc80e6b 100644
--- a/Orange/widgets/utils/tests/test_stickygraphicsview.py
+++ b/Orange/widgets/utils/tests/test_stickygraphicsview.py
@@ -121,16 +121,8 @@ def qWheelScroll(
     if pos.isNull():
         pos = widget.rect().center()
     globalPos = widget.mapToGlobal(pos)
-
-    if angleDelta.y() >= angleDelta.x():
-        qt4orient = Qt.Vertical
-        qt4delta = angleDelta.y()
-    else:
-        qt4orient = Qt.Horizontal
-        qt4delta = angleDelta.x()
-
     event = QWheelEvent(
         QPointF(pos), QPointF(globalPos), QPoint(), angleDelta,
-        qt4delta, qt4orient, buttons, modifiers
+        buttons, modifiers, Qt.NoScrollPhase, False
     )
     QApplication.sendEvent(widget, event)
diff --git a/Orange/widgets/utils/textimport.py b/Orange/widgets/utils/textimport.py
index ffc82fbf06f..6d3fdfbbcfb 100644
--- a/Orange/widgets/utils/textimport.py
+++ b/Orange/widgets/utils/textimport.py
@@ -668,7 +668,7 @@ def __init__(self, *args, **kwargs):
         self.grouping_sep_edit_cb.setValidator(
             QRegularExpressionValidator(QRegularExpression(r"(\.|,| |')?"), self)
         )
-        self.grouping_sep_edit_cb.activated[str].connect(
+        self.grouping_sep_edit_cb.textActivated.connect(
             self.__group_sep_activated)
 
         self.decimal_sep_edit_cb = TextEditCombo(
@@ -680,7 +680,7 @@ def __init__(self, *args, **kwargs):
         self.decimal_sep_edit_cb.setValidator(
             QRegularExpressionValidator(QRegularExpression(r"(\.|,)"), self))
         self.decimal_sep_edit_cb.addItems([".", ","])
-        self.decimal_sep_edit_cb.activated[str].connect(
+        self.decimal_sep_edit_cb.textActivated.connect(
             self.__decimal_sep_activated)
 
         number_sep_layout.addWidget(QLabel("Grouping:"))
@@ -731,7 +731,7 @@ def __init__(self, *args, **kwargs):
             objectName="-error-overlay",
             visible=False,
         )
-        overlay.setLayout(QVBoxLayout(margin=0))
+        overlay.setLayout(QVBoxLayout())
         self.__error_label = label = QLabel(objectName="-error-text-label")
         overlay.layout().addWidget(label)
         overlay.setWidget(self.dataview.viewport())
@@ -1338,14 +1338,14 @@ def rowsInserted(self, parent, start, end):
         # type: (QModelIndex, int, int) -> None
         super().rowsInserted(parent, start, end)
         behavior = self.selectionBehavior()
-        if behavior & (QTableView.SelectColumns | QTableView.SelectRows):
+        if behavior in (QTableView.SelectColumns, QTableView.SelectRows):
             # extend the selection to the new rows
             smodel = self.selectionModel()
             selection = smodel.selection()
             command = QItemSelectionModel.Select
-            if behavior & QTableView.SelectRows:
+            if behavior == QTableView.SelectRows:
                 command |= QItemSelectionModel.Rows
-            if behavior & QTableView.SelectColumns:
+            if behavior == QTableView.SelectColumns:
                 command |= QItemSelectionModel.Columns
             smodel.select(selection, command)
 
@@ -1436,7 +1436,7 @@ def initStyleOption(self, option, index):
         # type: (QStyleOptionViewItem, QModelIndex) -> None
         super().initStyleOption(option, index)
         palette = option.palette
-        shadow = palette.color(QPalette.Foreground)  # type: QColor
+        shadow = palette.color(QPalette.WindowText)  # type: QColor
         if shadow.isValid():
             shadow.setAlphaF(0.1)
             option.backgroundBrush = QBrush(shadow, Qt.SolidPattern)
diff --git a/Orange/widgets/visualize/owsilhouetteplot.py b/Orange/widgets/visualize/owsilhouetteplot.py
index 19513e44e4f..30a67efc4b8 100644
--- a/Orange/widgets/visualize/owsilhouetteplot.py
+++ b/Orange/widgets/visualize/owsilhouetteplot.py
@@ -742,7 +742,7 @@ def __setup(self):
 
         font = self.font()
         font.setPixelSize(self.__barHeight)
-        foreground = self.palette().brush(QPalette.Foreground)
+        foreground = self.palette().brush(QPalette.WindowText)
         ax = AxisItem(parent=self, orientation="top", maxTickLength=7)
         ax.setRange(smin, smax)
         self.__topScale = ax
@@ -1151,7 +1151,7 @@ def sizeHint(self, which, constraint=QRectF()):
     def paint(self, painter, option, widget=None):
         # type: (QPainter, QStyleOptionGraphicsItem, Optional[QWidget]) -> None
         palette = self.palette()  # type: QPalette
-        color = palette.color(QPalette.Foreground)
+        color = palette.color(QPalette.WindowText)
         painter.setPen(QPen(color, 1))
         rect = self.contentsRect()
         center = rect.center()
diff --git a/Orange/widgets/visualize/owtreeviewer2d.py b/Orange/widgets/visualize/owtreeviewer2d.py
index bace9ec1aea..7ca41395eb1 100644
--- a/Orange/widgets/visualize/owtreeviewer2d.py
+++ b/Orange/widgets/visualize/owtreeviewer2d.py
@@ -244,7 +244,6 @@ def __init__(self, scene, *args):
         self.setFocusPolicy(Qt.WheelFocus)
         self.setRenderHint(QPainter.Antialiasing)
         self.setRenderHint(QPainter.TextAntialiasing)
-        self.setRenderHint(QPainter.HighQualityAntialiasing)
 
     def resizeEvent(self, event):
         super().resizeEvent(event)
diff --git a/Orange/widgets/visualize/tests/test_owbarplot.py b/Orange/widgets/visualize/tests/test_owbarplot.py
index 69b437016a4..0ff75962a85 100644
--- a/Orange/widgets/visualize/tests/test_owbarplot.py
+++ b/Orange/widgets/visualize/tests/test_owbarplot.py
@@ -374,9 +374,9 @@ def assertSelectedIndices(self, indices, data=None, widget=None):
         indices = self.widget.grouped_indices_inverted
         self.assertSetEqual(set(widget.graph.selection), set(indices))
         pens = widget.graph.bar_item.opts["pens"]
-        self.assertTrue(all([pen.style() == 2 for i, pen
+        self.assertTrue(all([pen.style() == Qt.DashLine for i, pen
                              in enumerate(pens) if i in indices]))
-        self.assertTrue(all([pen.style() == 1 for i, pen
+        self.assertTrue(all([pen.style() == Qt.SolidLine for i, pen
                              in enumerate(pens) if i not in indices]))
 
 
diff --git a/Orange/widgets/visualize/tests/test_owdistributions.py b/Orange/widgets/visualize/tests/test_owdistributions.py
index b0f8fdd971e..66c3ca2f1ea 100644
--- a/Orange/widgets/visualize/tests/test_owdistributions.py
+++ b/Orange/widgets/visualize/tests/test_owdistributions.py
@@ -6,6 +6,9 @@
 
 import numpy as np
 from AnyQt.QtCore import QItemSelection, Qt
+from AnyQt.QtWidgets import QCheckBox
+
+from orangewidget.utils.combobox import qcombobox_emit_activated
 
 from Orange.data import Table, Domain, DiscreteVariable
 from Orange.widgets.tests.base import WidgetTest
@@ -22,14 +25,12 @@ def setUp(self):
     def _set_cvar(self, cvar):
         combo = self.widget.controls.cvar
         self.widget.cvar = cvar
-        combo.activated[int].emit(combo.currentIndex())
-        combo.activated[str].emit(combo.currentText())
+        qcombobox_emit_activated(combo, combo.currentIndex())
 
     def _set_fitter(self, i):
         combo = self.widget.controls.fitted_distribution
         combo.setCurrentIndex(i)
-        combo.activated[int].emit(combo.currentIndex())
-        combo.activated[str].emit(combo.currentText())
+        qcombobox_emit_activated(combo, i)
 
     def _set_var(self, var):
         listview = self.widget.controls.var
@@ -43,8 +44,9 @@ def _set_var(self, var):
         selectionmodel.selectionChanged.emit(newselection, oldselection)
 
     @staticmethod
-    def _set_check(checkbox, value):
-        checkbox.setCheckState(value)
+    def _set_check(checkbox: QCheckBox, value: bool):
+        state = Qt.Checked if value else Qt.Unchecked
+        checkbox.setCheckState(state)
         checkbox.toggled[bool].emit(value)
 
     def _set_slider(self, i):
@@ -415,8 +417,6 @@ def test_controls_disabling(self):
         # changing them simultaneously doesn't significantly degrade the tests
         def test_plot_types_combinations(self):
             """Check that the widget doesn't crash at any plot combination"""
-            from AnyQt.QtWidgets import qApp
-
             widget = self.widget
             c = widget.controls
             self.send_signal(widget.Inputs.data, self.iris)
@@ -431,13 +431,11 @@ def test_plot_types_combinations(self):
                         self._set_check(c.stacked_columns, b)
                         self._set_check(c.show_probs, b)
                         self._set_check(c.sort_by_freq, b)
-                        qApp.processEvents()
+                        widget.grab()  # run layout and paint
     else:
         def test_plot_types_combinations(self):
             """Check that the widget doesn't crash at any plot combination"""
             # pylint: disable=too-many-nested-blocks
-            from AnyQt.QtWidgets import qApp
-
             widget = self.widget
             c = widget.controls
             set_chk = self._set_check
@@ -458,7 +456,7 @@ def test_plot_types_combinations(self):
                                         set_chk(c.stacked_columns, stack)
                                         set_chk(c.show_probs, show_probs)
                                         set_chk(c.sort_by_freq, sort_by_freq)
-                                        qApp.processEvents()
+                                        widget.grab()  # run layout and paint
 
     def test_selection_grouping(self):
         """Widget groups consecutive selected bars"""
diff --git a/Orange/widgets/visualize/tests/test_owmosaic.py b/Orange/widgets/visualize/tests/test_owmosaic.py
index 577fdd5192b..262a8f441c3 100644
--- a/Orange/widgets/visualize/tests/test_owmosaic.py
+++ b/Orange/widgets/visualize/tests/test_owmosaic.py
@@ -4,7 +4,7 @@
 
 import numpy as np
 
-from AnyQt.QtCore import QEvent, QPoint, Qt
+from AnyQt.QtCore import QEvent, QPointF, Qt
 from AnyQt.QtGui import QMouseEvent
 
 from Orange.data import Table, DiscreteVariable, Domain, ContinuousVariable, \
@@ -36,8 +36,8 @@ def test_empty_column(self):
 
     def _select_data(self):
         self.widget.select_area(1, QMouseEvent(
-            QEvent.MouseButtonPress, QPoint(), Qt.LeftButton,
-            Qt.LeftButton, Qt.KeyboardModifiers()))
+            QEvent.MouseButtonPress, QPointF(), Qt.LeftButton,
+            Qt.LeftButton, Qt.NoModifier))
         return [2, 3, 9, 23, 29, 30, 34, 35, 37, 42, 47, 49]
 
     def test_continuous_metas(self):
@@ -150,8 +150,8 @@ def test_selection_setting(self):
 
         widget.select_area(
             1,
-            QMouseEvent(QEvent.MouseButtonPress, QPoint(), Qt.LeftButton,
-                        Qt.LeftButton, Qt.KeyboardModifiers()))
+            QMouseEvent(QEvent.MouseButtonPress, QPointF(), Qt.LeftButton,
+                        Qt.LeftButton, Qt.NoModifier))
 
         # Changing the data must reset the selection
         self.send_signal(widget.Inputs.data, Table("titanic"))
@@ -164,8 +164,8 @@ def test_selection_setting(self):
 
         widget.select_area(
             1,
-            QMouseEvent(QEvent.MouseButtonPress, QPoint(), Qt.LeftButton,
-                        Qt.LeftButton, Qt.KeyboardModifiers()))
+            QMouseEvent(QEvent.MouseButtonPress, QPointF(), Qt.LeftButton,
+                        Qt.LeftButton, Qt.NoModifier))
         settings = self.widget.settingsHandler.pack_data(self.widget)
 
         # Setting data to None must reset the selection
@@ -372,7 +372,7 @@ def test_max_attr_combo_1_disabling(self):
         vizrank.max_attrs = 0
         simulate.combobox_activate_index(self.widget.controls.variable_color, 0)
         self.assertEqual(vizrank.max_attrs, 1)
-        self.assertEqual(int(model.item(0).flags() & enabled), 0)
+        self.assertEqual(model.item(0).flags() & enabled, Qt.NoItemFlags)
 
         simulate.combobox_activate_index(self.widget.controls.variable_color, 1)
         self.assertEqual(vizrank.max_attrs, 1)
diff --git a/Orange/widgets/visualize/tests/test_owscatterplot.py b/Orange/widgets/visualize/tests/test_owscatterplot.py
index b2974508b1d..b5928674db9 100644
--- a/Orange/widgets/visualize/tests/test_owscatterplot.py
+++ b/Orange/widgets/visualize/tests/test_owscatterplot.py
@@ -975,13 +975,13 @@ def test_add_line_calls_proper_regressor(self):
 
         graph.orthonormal_regression = True
         graph._add_line(x, y, c)
-        graph._orthonormal_line.assert_called_once_with(x, y, c, 3, 1)
+        graph._orthonormal_line.assert_called_once_with(x, y, c, 3, Qt.SolidLine)
         graph._regression_line.assert_not_called()
         graph._orthonormal_line.reset_mock()
 
         graph.orthonormal_regression = False
         graph._add_line(x, y, c)
-        graph._regression_line.assert_called_with(x, y, c, 3, 1)
+        graph._regression_line.assert_called_with(x, y, c, 3, Qt.SolidLine)
         graph._orthonormal_line.assert_not_called()
 
     def test_no_regression_line(self):
diff --git a/Orange/widgets/visualize/tests/test_owscatterplotbase.py b/Orange/widgets/visualize/tests/test_owscatterplotbase.py
index eeb8cdcf3f4..07a6baf4b66 100644
--- a/Orange/widgets/visualize/tests/test_owscatterplotbase.py
+++ b/Orange/widgets/visualize/tests/test_owscatterplotbase.py
@@ -1434,7 +1434,7 @@ def select(modifiers, indices):
                     graph.update_labels.assert_not_called()
                 self.master.selection_changed.assert_called_with()
 
-        select(0, [7, 8, 9])
+        select(Qt.NoModifier, [7, 8, 9])
         np.testing.assert_almost_equal(
             graph.selection, [0, 0, 0, 0, 0, 0, 0, 1, 1, 1])
 
@@ -1450,12 +1450,12 @@ def select(modifiers, indices):
         np.testing.assert_almost_equal(
             graph.selection, [0, 0, 0, 0, 2, 2, 1, 0, 1, 1])
 
-        select(0, [1, 8])
+        select(Qt.NoModifier, [1, 8])
         np.testing.assert_almost_equal(
             graph.selection, [0, 1, 0, 0, 0, 0, 0, 0, 1, 0])
 
         graph.label_only_selected = False
-        select(0, [3, 4])
+        select(Qt.NoModifier, [3, 4])
 
     def test_unselect_all(self):
         graph = self.graph
diff --git a/Orange/widgets/visualize/tests/test_owsieve.py b/Orange/widgets/visualize/tests/test_owsieve.py
index 3aab7721e04..3d6b21f28f0 100644
--- a/Orange/widgets/visualize/tests/test_owsieve.py
+++ b/Orange/widgets/visualize/tests/test_owsieve.py
@@ -6,7 +6,7 @@
 
 import numpy as np
 
-from AnyQt.QtCore import QEvent, QPoint, Qt
+from AnyQt.QtCore import QEvent, QPointF, Qt
 from AnyQt.QtGui import QMouseEvent
 
 from Orange.data import ContinuousVariable, DiscreteVariable, Domain, Table
@@ -79,8 +79,8 @@ def _select_data(self):
         self.widget.attr_x, self.widget.attr_y = self.data.domain[:2]
         area = self.widget.areas[0]
         self.widget.select_area(area, QMouseEvent(
-            QEvent.MouseButtonPress, QPoint(), Qt.LeftButton,
-            Qt.LeftButton, Qt.KeyboardModifiers()))
+            QEvent.MouseButtonPress, QPointF(), Qt.LeftButton,
+            Qt.LeftButton, Qt.NoModifier))
         return [0, 4, 6, 7, 11, 17, 19, 21, 22, 24, 26, 39, 40, 43, 44, 46]
 
     def test_missing_values(self):
diff --git a/Orange/widgets/visualize/utils/customizableplot.py b/Orange/widgets/visualize/utils/customizableplot.py
index 6eb874ef255..e0c982478b9 100644
--- a/Orange/widgets/visualize/utils/customizableplot.py
+++ b/Orange/widgets/visualize/utils/customizableplot.py
@@ -27,7 +27,7 @@ def available_font_families() -> List:
     """
     if not QApplication.instance():
         _ = QApplication(sys.argv)
-    fonts = QFontDatabase().families()
+    fonts = QFontDatabase.families()
     default = default_font_family()
 
     defaults = [default]
diff --git a/Orange/widgets/visualize/utils/heatmap.py b/Orange/widgets/visualize/utils/heatmap.py
index 29782bb946e..4a02765d5bb 100644
--- a/Orange/widgets/visualize/utils/heatmap.py
+++ b/Orange/widgets/visualize/utils/heatmap.py
@@ -956,7 +956,7 @@ def __update_selection_geometry(self):
         self.__selection_manager.update_selection_rects()
         rects = self.__selection_manager.selection_rects
         palette = self.palette()
-        pen = QPen(palette.color(QPalette.Foreground), 2)
+        pen = QPen(palette.color(QPalette.WindowText), 2)
         pen.setCosmetic(True)
         brushcolor = QColor(palette.color(QPalette.Highlight))
         brushcolor.setAlpha(50)
diff --git a/Orange/widgets/visualize/utils/tests/test_customizableplot.py b/Orange/widgets/visualize/utils/tests/test_customizableplot.py
index 5863ced5fa3..c3566e26482 100644
--- a/Orange/widgets/visualize/utils/tests/test_customizableplot.py
+++ b/Orange/widgets/visualize/utils/tests/test_customizableplot.py
@@ -12,13 +12,13 @@ def test_available_font_families(self):
             font.return_value.family = Mock(return_value="mock regular")
 
             db.return_value = Mock()
-            db.return_value.families = Mock(
+            db.families = Mock(
                 return_value=["a", ".d", "e", ".b", "mock regular", "c"])
             self.assertEqual(customizableplot.available_font_families(),
                              ["mock regular", "", "a", ".b", "c", ".d", "e"])
 
             db.return_value = Mock()
-            db.return_value.families = Mock(
+            db.families = Mock(
                 return_value=["a", ".d", "e", ".b", "mock regular",
                               "mock bold", "mock italic", "c", "mock semi"])
             self.assertEqual(customizableplot.available_font_families(),
diff --git a/requirements-gui.txt b/requirements-gui.txt
index a7880c6961d..61a44d798d9 100644
--- a/requirements-gui.txt
+++ b/requirements-gui.txt
@@ -1,7 +1,7 @@
-orange-canvas-core>=0.1.24,<0.2a
-orange-widget-base>=4.16.1
+orange-canvas-core>=0.1.26,<0.2a
+orange-widget-base>=4.17.0
 
-AnyQt>=0.0.13
+AnyQt>=0.1.0
 
 # ignore pyqtgraph 0.12.4 due to https://github.com/pyqtgraph/pyqtgraph/issues/2237
 pyqtgraph>=0.12.2,!=0.12.4
diff --git a/tox.ini b/tox.ini
index 4871fd44b25..226447346e6 100644
--- a/tox.ini
+++ b/tox.ini
@@ -40,9 +40,9 @@ deps =
     latest: https://github.com/pyqtgraph/pyqtgraph/archive/refs/heads/master.zip#egg=pyqtgraph
     latest: https://github.com/biolab/orange-canvas-core/archive/refs/heads/master.zip#egg=orange-canvas-core
     latest: https://github.com/biolab/orange-widget-base/archive/refs/heads/master.zip#egg=orange-widget-base
-    oldest: orange-canvas-core==0.1.24
-    oldest: orange-widget-base==4.16.1
-    oldest: AnyQt==0.0.13
+    oldest: orange-canvas-core==0.1.26
+    oldest: orange-widget-base==4.17.0
+    oldest: AnyQt==0.1.0
     oldest: pyqtgraph==0.11.1
     oldest: matplotlib==2.2.5
     oldest: qtconsole==4.7.2
@@ -80,6 +80,21 @@ commands =
     coverage combine
     coverage report
 
+[testenv:pyqt6]
+changedir =
+    {envsitepackagesdir}
+setenv =
+    QT_API=PyQt6
+    ANYQT_HOOK_DENY=pyqt5
+deps =
+    PyQt6==6.2.*
+    PyQt6-Qt6==6.2.*
+    PyQt6-WebEngine==6.2.*
+    PyQt6-WebEngine-Qt6==6.2.*
+
+commands =
+    python -m unittest Orange.widgets.tests
+
 [testenv:add-ons]
 deps =
     {[testenv]deps}