diff --git a/pyproject.toml b/pyproject.toml
index 2550c5b..e7c901c 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -30,7 +30,7 @@ Download = "https://pypi.org/project/validate-pyproject/#files"
 
 [project.optional-dependencies]
 all = [
-    "packaging>=20.4",
+    "packaging>=24.2",
     "tomli>=1.2.1; python_version<'3.11'",
     "trove-classifiers>=2021.10.20",
 ]
diff --git a/src/validate_pyproject/formats.py b/src/validate_pyproject/formats.py
index 39320a8..1cf4a46 100644
--- a/src/validate_pyproject/formats.py
+++ b/src/validate_pyproject/formats.py
@@ -378,7 +378,25 @@ def int(value: builtins.int) -> bool:
     return -(2**63) <= value < 2**63
 
 
-def SPDX(value: str) -> bool:
-    """Should validate eventually"""
-    # TODO: validate conditional to the presence of (the right version) of packaging
-    return True
+try:
+    from packaging import licenses as _licenses
+
+    def SPDX(value: str) -> bool:
+        """See :ref:`PyPA's License-Expression specification
+        <pypa:core-metadata-license-expression>` (added in :pep:`639`).
+        """
+        try:
+            _licenses.canonicalize_license_expression(value)
+            return True
+        except _licenses.InvalidLicenseExpression:
+            return False
+
+except ImportError:  # pragma: no cover
+    _logger.warning(
+        "Could not find an up-to-date installation of `packaging`. "
+        "License expressions might not be validated. "
+        "To enforce validation, please install `packaging>=24.2`."
+    )
+
+    def SPDX(value: str) -> bool:
+        return True
diff --git a/tests/examples/simple/pep638.toml b/tests/examples/simple/pep639.toml
similarity index 100%
rename from tests/examples/simple/pep638.toml
rename to tests/examples/simple/pep639.toml
diff --git a/tests/invalid-examples/simple/pep639.errors.txt b/tests/invalid-examples/simple/pep639.errors.txt
new file mode 100644
index 0000000..e371926
--- /dev/null
+++ b/tests/invalid-examples/simple/pep639.errors.txt
@@ -0,0 +1 @@
+`project.license` must be valid exactly by one definition (0 matches found)
diff --git a/tests/invalid-examples/simple/pep639.toml b/tests/invalid-examples/simple/pep639.toml
new file mode 100644
index 0000000..8b30929
--- /dev/null
+++ b/tests/invalid-examples/simple/pep639.toml
@@ -0,0 +1,5 @@
+[project]
+name = "example"
+version = "1.2.3"
+license = "Apache Software License"  # should be "Apache-2.0"
+license-files = ["licenses/LICENSE"]
diff --git a/tests/test_formats.py b/tests/test_formats.py
index bd6965f..cdff3ee 100644
--- a/tests/test_formats.py
+++ b/tests/test_formats.py
@@ -293,6 +293,54 @@ def test_invalid_module_name_relaxed(example):
     assert formats.python_module_name_relaxed(example) is False
 
 
+@pytest.mark.parametrize(
+    "example",
+    [
+        "MIT",
+        "Bsd-3-clause",
+        "mit and (apache-2.0 or bsd-2-clause)",
+        "MIT OR GPL-2.0-or-later OR (FSFUL AND BSD-2-Clause)",
+        "GPL-3.0-only WITH Classpath-exception-2.0 OR BSD-3-Clause",
+        "LicenseRef-Special-License OR CC0-1.0 OR Unlicense",
+        "LicenseRef-Public-Domain",
+        "licenseref-proprietary",
+        "LicenseRef-Beerware-4.2",
+        "(LicenseRef-Special-License OR LicenseRef-OtherLicense) OR Unlicense",
+    ],
+)
+def test_valid_pep639_license_expression(example):
+    assert formats.SPDX(example) is True
+
+
+@pytest.mark.parametrize(
+    "example",
+    [
+        "",
+        "Use-it-after-midnight",
+        "LicenseRef-License with spaces",
+        "LicenseRef-License_with_underscores",
+        "or",
+        "and",
+        "with",
+        "mit or",
+        "mit and",
+        "mit with",
+        "or mit",
+        "and mit",
+        "with mit",
+        "(mit",
+        "mit)",
+        "mit or or apache-2.0",
+        # Missing an operator before `(`.
+        "mit or apache-2.0 (bsd-3-clause and MPL-2.0)",
+        # "2-BSD-Clause is not a valid license.
+        "Apache-2.0 OR 2-BSD-Clause",
+    ],
+)
+def test_invalid_pep639_license_expression(example):
+    assert formats.SPDX(example) is False
+
+
 class TestClassifiers:
     """The ``_TroveClassifier`` class and ``_download_classifiers`` are part of the
     private API and therefore need to be tested.