diff --git a/.github/workflows/compliance.yml b/.github/workflows/compliance.yml
new file mode 100644
index 0000000..77e6b05
--- /dev/null
+++ b/.github/workflows/compliance.yml
@@ -0,0 +1,27 @@
+on:
+  pull_request:
+    branches:
+      - main
+name: unittest
+jobs:
+  compliance:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python: ['3.10']
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+    - name: Setup Python
+      uses: actions/setup-python@v3
+      with:
+        python-version: ${{ matrix.python }}
+    - name: Install nox
+      run: |
+        python -m pip install --upgrade setuptools pip wheel
+        python -m pip install nox
+    - name: Run compliance tests
+      env:
+        COVERAGE_FILE: .coverage-compliance-${{ matrix.python }}
+      run: |
+        nox -s compliance
diff --git a/db_dtypes/core.py b/db_dtypes/core.py
index a06c6d6..b5b0b7a 100644
--- a/db_dtypes/core.py
+++ b/db_dtypes/core.py
@@ -17,7 +17,7 @@
 import numpy
 import pandas
 import pandas.api.extensions
-from pandas.api.types import is_dtype_equal, is_list_like, pandas_dtype
+from pandas.api.types import is_dtype_equal, is_list_like, is_scalar, pandas_dtype
 
 from db_dtypes import pandas_backports
 
@@ -31,9 +31,14 @@ class BaseDatetimeDtype(pandas.api.extensions.ExtensionDtype):
     names = None
 
     @classmethod
-    def construct_from_string(cls, name):
+    def construct_from_string(cls, name: str):
+        if not isinstance(name, str):
+            raise TypeError(
+                f"'construct_from_string' expects a string, got {type(name)}"
+            )
+
         if name != cls.name:
-            raise TypeError()
+            raise TypeError(f"Cannot construct a '{cls.__name__}' from 'another_type'")
 
         return cls()
 
@@ -74,6 +79,11 @@ def astype(self, dtype, copy=True):
         return super().astype(dtype, copy=copy)
 
     def _cmp_method(self, other, op):
+        """Compare array values, for use in OpsMixin."""
+
+        if is_scalar(other) and (pandas.isna(other) or type(other) == self.dtype.type):
+            other = type(self)([other])
+
         oshape = getattr(other, "shape", None)
         if oshape != self.shape and oshape != (1,) and self.shape != (1,):
             raise TypeError(
diff --git a/noxfile.py b/noxfile.py
index 5f48361..54421d8 100644
--- a/noxfile.py
+++ b/noxfile.py
@@ -37,6 +37,7 @@
 nox.options.sessions = [
     "lint",
     "unit",
+    "compliance",
     "cover",
     "lint_setup_py",
     "blacken",
@@ -77,7 +78,7 @@ def lint_setup_py(session):
     session.run("python", "setup.py", "check", "--restructuredtext", "--strict")
 
 
-def default(session):
+def default(session, tests_path):
     # Install all test dependencies, then install this package in-place.
 
     constraints_path = str(
@@ -106,15 +107,21 @@ def default(session):
         "--cov-config=.coveragerc",
         "--cov-report=",
         "--cov-fail-under=0",
-        os.path.join("tests", "unit"),
+        tests_path,
         *session.posargs,
     )
 
 
+@nox.session(python=UNIT_TEST_PYTHON_VERSIONS[-1])
+def compliance(session):
+    """Run the compliance test suite."""
+    default(session, os.path.join("tests", "compliance"))
+
+
 @nox.session(python=UNIT_TEST_PYTHON_VERSIONS)
 def unit(session):
     """Run the unit test suite."""
-    default(session)
+    default(session, os.path.join("tests", "unit"))
 
 
 @nox.session(python=SYSTEM_TEST_PYTHON_VERSIONS)
diff --git a/owlbot.py b/owlbot.py
index 30f3b3d..6c59671 100644
--- a/owlbot.py
+++ b/owlbot.py
@@ -64,11 +64,39 @@
 new_sessions = """
     "lint",
     "unit",
+    "compliance",
     "cover",
 """
 
 s.replace(["noxfile.py"], old_sessions, new_sessions)
 
+# Add compliance tests.
+s.replace(
+    ["noxfile.py"], r"def default\(session\):", "def default(session, tests_path):"
+)
+s.replace(["noxfile.py"], r'os.path.join\("tests", "unit"\),', "tests_path,")
+s.replace(
+    ["noxfile.py"],
+    r'''
+@nox.session\(python=UNIT_TEST_PYTHON_VERSIONS\)
+def unit\(session\):
+    """Run the unit test suite."""
+    default\(session\)
+''',
+    '''
+@nox.session(python=UNIT_TEST_PYTHON_VERSIONS[-1])
+def compliance(session):
+    """Run the compliance test suite."""
+    default(session, os.path.join("tests", "compliance"))
+
+
+@nox.session(python=UNIT_TEST_PYTHON_VERSIONS)
+def unit(session):
+    """Run the unit test suite."""
+    default(session, os.path.join("tests", "unit"))
+''',
+)
+
 # ----------------------------------------------------------------------------
 # Samples templates
 # ----------------------------------------------------------------------------
diff --git a/tests/compliance/conftest.py b/tests/compliance/conftest.py
new file mode 100644
index 0000000..bc76692
--- /dev/null
+++ b/tests/compliance/conftest.py
@@ -0,0 +1,53 @@
+# Copyright 2022 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import pandas
+import pytest
+
+
+@pytest.fixture(params=["ffill", "bfill"])
+def fillna_method(request):
+    """
+    Parametrized fixture giving method parameters 'ffill' and 'bfill' for
+    Series.fillna(method=<method>) testing.
+
+    See:
+    https://github.com/pandas-dev/pandas/blob/main/pandas/tests/extension/conftest.py
+    """
+    return request.param
+
+
+@pytest.fixture
+def na_value():
+    return pandas.NaT
+
+
+@pytest.fixture
+def na_cmp():
+    """
+    Binary operator for comparing NA values.
+
+    Should return a function of two arguments that returns
+    True if both arguments are (scalar) NA for your type.
+
+    See:
+    https://github.com/pandas-dev/pandas/blob/main/pandas/tests/extension/conftest.py
+    and
+    https://github.com/pandas-dev/pandas/blob/main/pandas/tests/extension/test_datetime.py
+    """
+
+    def cmp(a, b):
+        return a is pandas.NaT and a is b
+
+    return cmp
diff --git a/tests/compliance/date/conftest.py b/tests/compliance/date/conftest.py
new file mode 100644
index 0000000..e25ccc9
--- /dev/null
+++ b/tests/compliance/date/conftest.py
@@ -0,0 +1,47 @@
+# Copyright 2022 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import datetime
+
+import numpy
+import pytest
+
+from db_dtypes import DateArray, DateDtype
+
+
+@pytest.fixture
+def data():
+    return DateArray(
+        numpy.arange(
+            datetime.datetime(1900, 1, 1),
+            datetime.datetime(2099, 12, 31),
+            datetime.timedelta(days=731),
+            dtype="datetime64[ns]",
+        )
+    )
+
+
+@pytest.fixture
+def data_missing():
+    """Length-2 array with [NA, Valid]
+
+    See:
+    https://github.com/pandas-dev/pandas/blob/main/pandas/tests/extension/conftest.py
+    """
+    return DateArray([None, datetime.date(2022, 1, 27)])
+
+
+@pytest.fixture
+def dtype():
+    return DateDtype()
diff --git a/tests/compliance/date/test_date_compliance.py b/tests/compliance/date/test_date_compliance.py
new file mode 100644
index 0000000..a805ecd
--- /dev/null
+++ b/tests/compliance/date/test_date_compliance.py
@@ -0,0 +1,47 @@
+# Copyright 2022 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""
+Tests for extension interface compliance, inherited from pandas.
+
+See:
+https://github.com/pandas-dev/pandas/blob/main/pandas/tests/extension/decimal/test_decimal.py
+and
+https://github.com/pandas-dev/pandas/blob/main/pandas/tests/extension/test_period.py
+"""
+
+from pandas.tests.extension import base
+
+
+class TestDtype(base.BaseDtypeTests):
+    pass
+
+
+class TestInterface(base.BaseInterfaceTests):
+    pass
+
+
+class TestConstructors(base.BaseConstructorsTests):
+    pass
+
+
+class TestReshaping(base.BaseReshapingTests):
+    pass
+
+
+class TestGetitem(base.BaseGetitemTests):
+    pass
+
+
+class TestMissing(base.BaseMissingTests):
+    pass
diff --git a/tests/unit/test_date.py b/tests/unit/test_date.py
index bf877ea..bce2dc1 100644
--- a/tests/unit/test_date.py
+++ b/tests/unit/test_date.py
@@ -13,15 +13,27 @@
 # limitations under the License.
 
 import datetime
+import operator
 
 import pandas
+import pandas.testing
 import pytest
 
-# To register the types.
-import db_dtypes  # noqa
+import db_dtypes
 from db_dtypes import pandas_backports
 
 
+def test_construct_from_string_with_nonstring():
+    with pytest.raises(TypeError):
+        db_dtypes.DateDtype.construct_from_string(object())
+
+
+def test__cmp_method_with_scalar():
+    input_array = db_dtypes.DateArray([datetime.date(1900, 1, 1)])
+    got = input_array._cmp_method(datetime.date(1900, 1, 1), operator.eq)
+    assert got[0]
+
+
 @pytest.mark.parametrize(
     "value, expected",
     [