diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index b1a1a7d9..3989946b 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -13,8 +13,16 @@ jobs:
       fail-fast: false
       matrix:
         python-version: ["3.11", "3.12", "3.13"]
+        # Run full test matrix on latest version of zarr
+        zarr-version: ["3.1.*"]
         # macos-13 is an intel runner, macos-14 is an arm64 runner
-        platform: [ubuntu-latest, ubuntu-22.04-arm, windows-latest, macos-13, macos-14]
+        platform:
+          [ubuntu-latest, ubuntu-22.04-arm, windows-latest, macos-13, macos-14]
+        include:
+          # Add one test run for zarr 3.0.x
+          - python-version: "3.12"
+            zarr-version: "3.0.*"
+            platform: "ubuntu-latest"
 
     defaults:
       run:
@@ -26,6 +34,7 @@ jobs:
         with:
           submodules: recursive
           fetch-depth: 0 # required for version resolution
+          fetch-tags: true
 
       - name: Set up Conda
         uses: conda-incubator/setup-miniconda@v3.1.1
@@ -56,14 +65,14 @@ jobs:
         # Since zarr v3 requires numpy >= 1.25, on Python 3.11 leave it out
         # so we can have some tests of our minimum version of numpy (1.24)
         if: matrix.python-version != '3.11'
-        run: python -m pip install zarr>=3
+        run: python -m pip install zarr==${{ matrix.zarr-version }}
 
       - name: List installed packages
         run: python -m pip list
 
       - name: Run tests
         shell: "bash -l {0}"
-        run: pytest -v
+        run: pytest -v --pyargs numcodecs.tests
 
       - uses: codecov/codecov-action@v5
         with:
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index c08b8f8a..c6b0ab6c 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -30,4 +30,4 @@ repos:
       hooks:
       -   id: mypy
           args: [--config-file, pyproject.toml]
-          additional_dependencies: [numpy, pytest, crc32c, zfpy, 'zarr>=3']
+          additional_dependencies: [numpy, pytest, crc32c, zfpy, 'zarr>=3.1']
diff --git a/numcodecs/zarr3.py b/numcodecs/zarr3.py
index 3ace9814..3384c3e6 100644
--- a/numcodecs/zarr3.py
+++ b/numcodecs/zarr3.py
@@ -29,19 +29,21 @@
 import math
 from dataclasses import dataclass, replace
 from functools import cached_property
-from typing import Any, Self
+from importlib.metadata import version
+from typing import TYPE_CHECKING, Any, Self
 from warnings import warn
 
 import numpy as np
+from packaging.version import Version
 
 import numcodecs
 
 try:
-    import zarr
+    import zarr  # noqa: F401
 
-    if zarr.__version__ < "3.0.0":  # pragma: no cover
+    if Version(version('zarr')) < Version("3.0.0"):
         raise ImportError("zarr 3.0.0 or later is required to use the numcodecs zarr integration.")
-except ImportError as e:  # pragma: no cover
+except ImportError as e:
     raise ImportError(
         "zarr 3.0.0 or later is required to use the numcodecs zarr integration."
     ) from e
@@ -53,14 +55,32 @@
 from zarr.core.buffer.cpu import as_numpy_array_wrapper
 from zarr.core.common import JSON, parse_named_configuration, product
 
+if TYPE_CHECKING:
+    from zarr.dtype import ZDType
+
 CODEC_PREFIX = "numcodecs."
 
 
+def _from_zarr_dtype(dtype: Any) -> np.dtype:
+    """
+    Get a numpy data type from an array spec, depending on the zarr version.
+    """
+    if Version(version('zarr')) >= Version("3.1.0"):
+        return dtype.to_native_dtype()
+    return dtype
+
+
+def _to_zarr_dtype(dtype: np.dtype) -> Any:
+    if Version(version('zarr')) >= Version("3.1.0"):
+        from zarr.dtype import parse_data_type
+
+        return parse_data_type(dtype, zarr_format=3)
+    return dtype
+
+
 def _expect_name_prefix(codec_name: str) -> str:
     if not codec_name.startswith(CODEC_PREFIX):
-        raise ValueError(
-            f"Expected name to start with '{CODEC_PREFIX}'. Got {codec_name} instead."
-        )  # pragma: no cover
+        raise ValueError(f"Expected name to start with '{CODEC_PREFIX}'. Got {codec_name} instead.")
     return codec_name.removeprefix(CODEC_PREFIX)
 
 
@@ -69,7 +89,7 @@ def _parse_codec_configuration(data: dict[str, JSON]) -> dict[str, JSON]:
     if not parsed_name.startswith(CODEC_PREFIX):
         raise ValueError(
             f"Expected name to start with '{CODEC_PREFIX}'. Got {parsed_name} instead."
-        )  # pragma: no cover
+        )
     id = _expect_name_prefix(parsed_name)
     return {"id": id, **parsed_configuration}
 
@@ -95,7 +115,7 @@ def __init__(self, **codec_config: JSON) -> None:
         if not self.codec_name:
             raise ValueError(
                 "The codec name needs to be supplied through the `codec_name` attribute."
-            )  # pragma: no cover
+            )
         unprefixed_codec_name = _expect_name_prefix(self.codec_name)
 
         if "id" not in codec_config:
@@ -103,7 +123,7 @@ def __init__(self, **codec_config: JSON) -> None:
         elif codec_config["id"] != unprefixed_codec_name:
             raise ValueError(
                 f"Codec id does not match {unprefixed_codec_name}. Got: {codec_config['id']}."
-            )  # pragma: no cover
+            )
 
         object.__setattr__(self, "codec_config", codec_config)
         warn(
@@ -224,7 +244,8 @@ class LZMA(_NumcodecsBytesBytesCodec, codec_name="lzma"):
 class Shuffle(_NumcodecsBytesBytesCodec, codec_name="shuffle"):
     def evolve_from_array_spec(self, array_spec: ArraySpec) -> Shuffle:
         if self.codec_config.get("elementsize") is None:
-            return Shuffle(**{**self.codec_config, "elementsize": array_spec.dtype.itemsize})
+            dtype = _from_zarr_dtype(array_spec.dtype)
+            return Shuffle(**{**self.codec_config, "elementsize": dtype.itemsize})
         return self  # pragma: no cover
 
 
@@ -232,7 +253,8 @@ def evolve_from_array_spec(self, array_spec: ArraySpec) -> Shuffle:
 class Delta(_NumcodecsArrayArrayCodec, codec_name="delta"):
     def resolve_metadata(self, chunk_spec: ArraySpec) -> ArraySpec:
         if astype := self.codec_config.get("astype"):
-            return replace(chunk_spec, dtype=np.dtype(astype))  # type: ignore[call-overload]
+            dtype = _to_zarr_dtype(np.dtype(astype))  # type: ignore[call-overload]
+            return replace(chunk_spec, dtype=dtype)
         return chunk_spec
 
 
@@ -243,12 +265,14 @@ class BitRound(_NumcodecsArrayArrayCodec, codec_name="bitround"):
 class FixedScaleOffset(_NumcodecsArrayArrayCodec, codec_name="fixedscaleoffset"):
     def resolve_metadata(self, chunk_spec: ArraySpec) -> ArraySpec:
         if astype := self.codec_config.get("astype"):
-            return replace(chunk_spec, dtype=np.dtype(astype))  # type: ignore[call-overload]
+            dtype = _to_zarr_dtype(np.dtype(astype))  # type: ignore[call-overload]
+            return replace(chunk_spec, dtype=dtype)
         return chunk_spec
 
     def evolve_from_array_spec(self, array_spec: ArraySpec) -> FixedScaleOffset:
         if self.codec_config.get("dtype") is None:
-            return FixedScaleOffset(**{**self.codec_config, "dtype": str(array_spec.dtype)})
+            dtype = _from_zarr_dtype(array_spec.dtype)
+            return FixedScaleOffset(**{**self.codec_config, "dtype": str(dtype)})
         return self
 
 
@@ -258,7 +282,8 @@ def __init__(self, **codec_config: JSON) -> None:
 
     def evolve_from_array_spec(self, array_spec: ArraySpec) -> Quantize:
         if self.codec_config.get("dtype") is None:
-            return Quantize(**{**self.codec_config, "dtype": str(array_spec.dtype)})
+            dtype = _from_zarr_dtype(array_spec.dtype)
+            return Quantize(**{**self.codec_config, "dtype": str(dtype)})
         return self
 
 
@@ -267,28 +292,31 @@ def resolve_metadata(self, chunk_spec: ArraySpec) -> ArraySpec:
         return replace(
             chunk_spec,
             shape=(1 + math.ceil(product(chunk_spec.shape) / 8),),
-            dtype=np.dtype("uint8"),
+            dtype=_to_zarr_dtype(np.dtype("uint8")),
         )
 
-    def validate(self, *, dtype: np.dtype[Any], **_kwargs) -> None:
-        if dtype != np.dtype("bool"):
+    def validate(self, *, shape: tuple[int, ...], dtype: "ZDType[Any, Any]", **_kwargs) -> None:  # noqa: UP037
+        _dtype = _from_zarr_dtype(dtype)
+        if _dtype != np.dtype("bool"):
             raise ValueError(f"Packbits filter requires bool dtype. Got {dtype}.")
 
 
 class AsType(_NumcodecsArrayArrayCodec, codec_name="astype"):
     def resolve_metadata(self, chunk_spec: ArraySpec) -> ArraySpec:
-        return replace(chunk_spec, dtype=np.dtype(self.codec_config["encode_dtype"]))  # type: ignore[arg-type]
+        dtype = _to_zarr_dtype(np.dtype(self.codec_config["encode_dtype"]))  # type: ignore[arg-type]
+        return replace(chunk_spec, dtype=dtype)
 
     def evolve_from_array_spec(self, array_spec: ArraySpec) -> AsType:
         if self.codec_config.get("decode_dtype") is None:
-            return AsType(**{**self.codec_config, "decode_dtype": str(array_spec.dtype)})
+            dtype = _from_zarr_dtype(array_spec.dtype)
+            return AsType(**{**self.codec_config, "decode_dtype": str(dtype)})
         return self
 
 
 # bytes-to-bytes checksum codecs
 class _NumcodecsChecksumCodec(_NumcodecsBytesBytesCodec):
     def compute_encoded_size(self, input_byte_length: int, chunk_spec: ArraySpec) -> int:
-        return input_byte_length + 4  # pragma: no cover
+        return input_byte_length + 4
 
 
 class CRC32(_NumcodecsChecksumCodec, codec_name="crc32"):
diff --git a/pyproject.toml b/pyproject.toml
index 387603f3..7ed4aefe 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -14,7 +14,7 @@ description = """
 A Python package providing buffer compression and transformation codecs \
 for use in data storage and communication applications."""
 readme = "README.rst"
-dependencies = ["numpy>=1.24", "typing_extensions"]
+dependencies = ["numpy>=1.24", "typing_extensions", "packaging"]
 requires-python = ">=3.11"
 dynamic = [
   "version",