diff --git a/.github/workflows/numpy.yml b/.github/workflows/numpy.yml
index 7e1eed7d..e4694fb0 100644
--- a/.github/workflows/numpy.yml
+++ b/.github/workflows/numpy.yml
@@ -22,41 +22,26 @@ jobs:
         python -m pip install git+https://github.com/numpy/numpy
         python -m pip install -r requirements.txt
     - name: Run the test suite
+      env:
+        ARRAY_API_TESTS_MODULE: numpy.array_api
       run: |
         # Mark some known issues as XFAIL
-        cat << EOF >> conftest.py
+        cat << EOF >> xfails.txt
+
+        # https://github.com/numpy/numpy/issues/18881
+        array_api_tests/test_creation_functions.py::test_linspace
+        # einsum is not yet completed in the spec
+        array_api_tests/test_signatures.py::test_has_names[einsum]
+        # dlpack support is not yet implemented in NumPy
+        # See https://github.com/numpy/numpy/pull/19083
+        array_api_tests/test_signatures.py::test_function_positional_args[__dlpack__]
+        array_api_tests/test_signatures.py::test_function_positional_args[__dlpack_device__]
+        array_api_tests/test_signatures.py::test_function_positional_args[from_dlpack]
+        array_api_tests/test_signatures.py::test_function_positional_args[to_device]
+        array_api_tests/test_signatures.py::test_function_keyword_only_args[__dlpack__]
+        # floor_divide has an issue related to https://github.com/data-apis/array-api/issues/264
+        array_api_tests/test_elementwise_functions.py::test_floor_divide
 
-        names_to_be_xfailed = (
-            # https://github.com/numpy/numpy/issues/18881
-            "array_api_tests/test_creation_functions.py::test_linspace",
-            # einsum is not yet completed in the spec
-            "array_api_tests/test_signatures.py::test_has_names[einsum]",
-            # The linalg extension is not yet implemented in NumPy
-            "array_api_tests/test_signatures.py::test_has_names[linalg]",
-            # dlpack support is not yet implemented in NumPy. https://github.com/numpy/numpy/pull/19083
-            "array_api_tests/test_signatures.py::test_function_positional_args[__dlpack__]",
-            "array_api_tests/test_signatures.py::test_function_positional_args[__dlpack_device__]",
-            "array_api_tests/test_signatures.py::test_function_positional_args[from_dlpack]",
-            "array_api_tests/test_signatures.py::test_function_keyword_only_args[__dlpack__]",
-
-            # Updates to the spec since the last change to numpy.array_api.
-            # These will fail until NumPy is updated.
-            "array_api_tests/test_signatures.py::test_has_names[__index__]",
-            "array_api_tests/test_signatures.py::test_has_names[to_device]",
-            "array_api_tests/test_signatures.py::test_has_names[mT]",
-            "array_api_tests/test_signatures.py::test_has_names[tril]",
-            "array_api_tests/test_signatures.py::test_has_names[triu]",
-            "array_api_tests/test_signatures.py::test_has_names[matrix_transpose]",
-            "array_api_tests/test_signatures.py::test_has_names[permute_dims]",
-            "array_api_tests/test_signatures.py::test_function_positional_args[__index__]",
-            "array_api_tests/test_signatures.py::test_function_keyword_only_args[prod]",
-            "array_api_tests/test_signatures.py::test_function_keyword_only_args[sum]",
-        )
-
-        def pytest_collection_modifyitems(config, items):
-            for item in items:
-                if item.nodeid in names_to_be_xfailed:
-                    item.add_marker("xfail")
         EOF
 
-        ARRAY_API_TESTS_MODULE=numpy.array_api pytest -v -rxXfE
+        pytest -v -rxXfE
diff --git a/README.md b/README.md
index bb641538..c8d30717 100644
--- a/README.md
+++ b/README.md
@@ -10,19 +10,23 @@ specification that are not yet tested here.
 
 ## Running the tests
 
+### Setup
+
 To run the tests, first install the testing dependencies
 
-    pip install pytest hypothesis numpy
+    pip install pytest hypothesis
 
 or
 
-    conda install pytest hypothesis numpy
+    conda install pytest hypothesis
+
+as well as the array libraries that you want to test. 
+
+### Specifying the array module
 
-as well as the array libraries that you want to test. (Note, in the future,
-NumPy will be removed as a dependency on the test suite). To run the tests,
-you need to set the array library that is to be tested. There are two ways to
-do this. One way is to set the `ARRAY_API_TESTS_MODULE` environment variable.
-For example
+To run the tests, you need to set the array library that is to be tested. There
+are two ways to do this. One way is to set the `ARRAY_API_TESTS_MODULE`
+environment variable. For example you can set it when running `pytest`
 
     ARRAY_API_TESTS_MODULE=numpy pytest
 
@@ -35,12 +39,21 @@ array_module = None
 
 to
 
-```
+```py
 import numpy as array_module
 ```
 
 (replacing `numpy` with the array module namespace to be tested).
 
+### Specifying test cases
+
+The test suite tries to logically organise its tests so you can find specific
+test cases whilst developing something in particular. So to avoid running the
+rather slow complete suite, you can specify particular test cases like any other
+test suite.
+
+    pytest array_api_tests/test_creation_functions.py::test_zeros
+
 ## Notes on Interpreting Errors
 
 - Some tests cannot be run unless other tests pass first. This is because very
@@ -66,6 +79,12 @@ import numpy as array_module
 
 ## Configuring Tests
 
+By default, tests for the optional Array API extensions such as
+[`linalg`](https://data-apis.org/array-api/latest/extensions/linear_algebra_functions.html)
+will be skipped if not present in the specified array module. You can purposely
+skip testing extension(s) via the `--disable-extension` option, and likewise
+purposely test them via the `--enable-extension` option.
+
 The tests make heavy use of the
 [Hypothesis](https://hypothesis.readthedocs.io/en/latest/) testing library.
 Hypothesis generates random input values for the tests. You can configure how
diff --git a/array_api_tests/meta_tests/__init__.py b/array_api_tests/meta/__init__.py
similarity index 100%
rename from array_api_tests/meta_tests/__init__.py
rename to array_api_tests/meta/__init__.py
diff --git a/array_api_tests/meta_tests/test_array_helpers.py b/array_api_tests/meta/test_array_helpers.py
similarity index 100%
rename from array_api_tests/meta_tests/test_array_helpers.py
rename to array_api_tests/meta/test_array_helpers.py
diff --git a/array_api_tests/meta_tests/test_hypothesis_helpers.py b/array_api_tests/meta/test_hypothesis_helpers.py
similarity index 100%
rename from array_api_tests/meta_tests/test_hypothesis_helpers.py
rename to array_api_tests/meta/test_hypothesis_helpers.py
diff --git a/array_api_tests/meta/test_utils.py b/array_api_tests/meta/test_utils.py
new file mode 100644
index 00000000..f4d7cf1f
--- /dev/null
+++ b/array_api_tests/meta/test_utils.py
@@ -0,0 +1,9 @@
+from ..test_signatures import extension_module
+
+
+def test_extension_module_is_extension():
+    assert extension_module('linalg')
+
+
+def test_extension_func_is_not_extension():
+    assert not extension_module('linalg.cross')
diff --git a/array_api_tests/test_linalg.py b/array_api_tests/test_linalg.py
index afd32f5c..421eeacd 100644
--- a/array_api_tests/test_linalg.py
+++ b/array_api_tests/test_linalg.py
@@ -13,6 +13,7 @@
 
 """
 
+import pytest
 from hypothesis import assume, given
 from hypothesis.strategies import (booleans, composite, none, tuples, integers,
                                    shared, sampled_from)
@@ -33,6 +34,7 @@
 from . import _array_module
 from ._array_module import linalg
 
+
 # Standin strategy for not yet implemented tests
 todo = none()
 
@@ -74,6 +76,7 @@ def _test_namedtuple(res, fields, func_name):
         assert hasattr(res, field), f"{func_name}() result namedtuple doesn't have the '{field}' field"
         assert res[i] is getattr(res, field), f"{func_name}() result namedtuple '{field}' field is not in position {i}"
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=positive_definite_matrices(),
     kw=kwargs(upper=booleans())
@@ -121,6 +124,7 @@ def cross_args(draw, dtype_objects=dh.numeric_dtypes):
     )
     return draw(arrays1), draw(arrays2), kw
 
+@pytest.mark.xp_extension('linalg')
 @given(
     cross_args()
 )
@@ -159,6 +163,7 @@ def test_cross(x1_x2_kw):
             ], dtype=res.dtype)
         assert_exactly_equal(res_stack, exact_cross)
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=xps.floating_dtypes(), shape=square_matrix_shapes),
 )
@@ -172,6 +177,7 @@ def test_det(x):
 
     # TODO: Test that res actually corresponds to the determinant of x
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=dtypes, shape=matrix_shapes),
     # offset may produce an overflow if it is too large. Supporting offsets
@@ -206,6 +212,7 @@ def true_diag(x_stack):
 
     _test_stacks(linalg.diagonal, x, **kw, res=res, dims=1, true_val=true_diag)
 
+@pytest.mark.xp_extension('linalg')
 @given(x=symmetric_matrices(finite=True))
 def test_eigh(x):
     res = linalg.eigh(x)
@@ -229,6 +236,7 @@ def test_eigh(x):
     # TODO: Test that res actually corresponds to the eigenvalues and
     # eigenvectors of x
 
+@pytest.mark.xp_extension('linalg')
 @given(x=symmetric_matrices(finite=True))
 def test_eigvalsh(x):
     res = linalg.eigvalsh(x)
@@ -242,6 +250,7 @@ def test_eigvalsh(x):
 
     # TODO: Test that res actually corresponds to the eigenvalues of x
 
+@pytest.mark.xp_extension('linalg')
 @given(x=invertible_matrices())
 def test_inv(x):
     res = linalg.inv(x)
@@ -286,6 +295,7 @@ def test_matmul(x1, x2):
         assert res.shape == stack_shape + (x1.shape[-2], x2.shape[-1])
         _test_stacks(_array_module.matmul, x1, x2, res=res)
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=xps.floating_dtypes(), shape=shapes),
     kw=kwargs(axis=todo, keepdims=todo, ord=todo)
@@ -295,6 +305,7 @@ def test_matrix_norm(x, kw):
     pass
 
 matrix_power_n = shared(integers(-1000, 1000), key='matrix_power n')
+@pytest.mark.xp_extension('linalg')
 @given(
     # Generate any square matrix if n >= 0 but only invertible matrices if n < 0
     x=matrix_power_n.flatmap(lambda n: invertible_matrices() if n < 0 else
@@ -316,6 +327,7 @@ def test_matrix_power(x, n):
     func = lambda x: linalg.matrix_power(x, n)
     _test_stacks(func, x, res=res, true_val=true_val)
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=xps.floating_dtypes(), shape=shapes),
     kw=kwargs(rtol=todo)
@@ -341,6 +353,7 @@ def test_matrix_transpose(x):
 
     _test_stacks(_array_module.matrix_transpose, x, res=res, true_val=true_val)
 
+@pytest.mark.xp_extension('linalg')
 @given(
     *two_mutual_arrays(dtype_objs=dh.numeric_dtypes,
                        two_shapes=tuples(one_d_shapes, one_d_shapes))
@@ -364,6 +377,7 @@ def test_outer(x1, x2):
 
     assert_exactly_equal(res, true_res)
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=xps.floating_dtypes(), shape=shapes),
     kw=kwargs(rtol=todo)
@@ -372,6 +386,7 @@ def test_pinv(x, kw):
     # res = linalg.pinv(x, **kw)
     pass
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=xps.floating_dtypes(), shape=matrix_shapes),
     kw=kwargs(mode=sampled_from(['reduced', 'complete']))
@@ -407,6 +422,7 @@ def test_qr(x, kw):
     # Check that r is upper-triangular.
     assert_exactly_equal(r, _array_module.triu(r))
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=xps.floating_dtypes(), shape=square_matrix_shapes),
 )
@@ -464,6 +480,7 @@ def x2_shapes(draw):
     x2 = xps.arrays(dtype=xps.floating_dtypes(), shape=x2_shapes())
     return x1, x2
 
+@pytest.mark.xp_extension('linalg')
 @given(*solve_args())
 def test_solve(x1, x2):
     # TODO: solve() is currently ambiguous, in that some inputs can be
@@ -476,6 +493,7 @@ def test_solve(x1, x2):
     # res = linalg.solve(x1, x2)
     pass
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=finite_matrices,
     kw=kwargs(full_matrices=booleans())
@@ -503,6 +521,7 @@ def test_svd(x, kw):
         assert u.shape == (*stack, M, K)
         assert vh.shape == (*stack, K, N)
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=xps.floating_dtypes(), shape=shapes),
 )
@@ -519,6 +538,7 @@ def test_tensordot(x1, x2, kw):
     # res = _array_module.tensordot(x1, x2, **kw)
     pass
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=xps.floating_dtypes(), shape=shapes),
     kw=kwargs(offset=todo)
@@ -536,6 +556,7 @@ def test_vecdot(x1, x2, kw):
     # res = _array_module.vecdot(x1, x2, **kw)
     pass
 
+@pytest.mark.xp_extension('linalg')
 @given(
     x=xps.arrays(dtype=xps.floating_dtypes(), shape=shapes),
     kw=kwargs(axis=todo, keepdims=todo, ord=todo)
diff --git a/array_api_tests/test_signatures.py b/array_api_tests/test_signatures.py
index e8106985..436701ab 100644
--- a/array_api_tests/test_signatures.py
+++ b/array_api_tests/test_signatures.py
@@ -26,7 +26,18 @@ def extension_module(name):
     if extension_module(n):
         extension_module_names.extend([f'{n}.{i}' for i in getattr(function_stubs, n).__all__])
 
-all_names = function_stubs.__all__ + extension_module_names
+
+params = []
+for name in function_stubs.__all__:
+    marks = []
+    if extension_module(name):
+        marks.append(pytest.mark.xp_extension(name))
+    params.append(pytest.param(name, marks=marks))
+for name in extension_module_names:
+    ext = name.split('.')[0]
+    mark = pytest.mark.xp_extension(ext)
+    params.append(pytest.param(name, marks=[mark]))
+
 
 def array_method(name):
     return stub_module(name) == 'array_object'
@@ -130,7 +141,7 @@ def example_argument(arg, func_name, dtype):
     else:
         raise RuntimeError(f"Don't know how to test argument {arg}. Please update test_signatures.py")
 
-@pytest.mark.parametrize('name', all_names)
+@pytest.mark.parametrize('name', params)
 def test_has_names(name):
     if extension_module(name):
         assert hasattr(mod, name), f'{mod_name} is missing the {name} extension'
@@ -146,7 +157,7 @@ def test_has_names(name):
     else:
         assert hasattr(mod, name), f"{mod_name} is missing the {function_category(name)} function {name}()"
 
-@pytest.mark.parametrize('name', all_names)
+@pytest.mark.parametrize('name', params)
 def test_function_positional_args(name):
     # Note: We can't actually test that positional arguments are
     # positional-only, as that would require knowing the argument name and
@@ -224,7 +235,7 @@ def test_function_positional_args(name):
             # NumPy ufuncs raise ValueError instead of TypeError
             raises((TypeError, ValueError), lambda: mod_func(*args[:n]), f"{name}() should not accept {n} positional arguments")
 
-@pytest.mark.parametrize('name', all_names)
+@pytest.mark.parametrize('name', params)
 def test_function_keyword_only_args(name):
     if extension_module(name):
         return
diff --git a/conftest.py b/conftest.py
index cd188b3d..804bab29 100644
--- a/conftest.py
+++ b/conftest.py
@@ -1,30 +1,56 @@
+from functools import lru_cache
+from pathlib import Path
+
+from pytest import mark
 from hypothesis import settings
 
-# Add a --hypothesis-max-examples flag to pytest. See
-# https://github.com/HypothesisWorks/hypothesis/issues/2434#issuecomment-630309150
+from array_api_tests import _array_module as xp
+from array_api_tests._array_module import _UndefinedStub
+
+
+settings.register_profile('xp_default', deadline=800)
+
 
 def pytest_addoption(parser):
-    # Add an option to change the Hypothesis max_examples setting.
+    # Hypothesis max examples
+    # See https://github.com/HypothesisWorks/hypothesis/issues/2434
     parser.addoption(
-        "--hypothesis-max-examples",
-        "--max-examples",
-        action="store",
+        '--hypothesis-max-examples',
+        '--max-examples',
+        action='store',
         default=None,
-        help="set the Hypothesis max_examples setting",
+        help='set the Hypothesis max_examples setting',
+    )
+    # Hypothesis deadline
+    parser.addoption(
+        '--hypothesis-disable-deadline',
+        '--disable-deadline',
+        action='store_true',
+        help='disable the Hypothesis deadline',
+    )
+    # enable/disable extensions
+    parser.addoption(
+        '--enable-extension',
+        metavar='ext',
+        nargs='+',
+        default=[],
+        help='enable testing for Array API extension(s)',
     )
-
-    # Add an option to disable the Hypothesis deadline
     parser.addoption(
-        "--hypothesis-disable-deadline",
-        "--disable-deadline",
-        action="store_true",
-        help="disable the Hypothesis deadline",
+        '--disable-extension',
+        metavar='ext',
+        nargs='+',
+        default=[],
+        help='disable testing for Array API extension(s)',
     )
 
 
 def pytest_configure(config):
-    # Set Hypothesis max_examples.
-    hypothesis_max_examples = config.getoption("--hypothesis-max-examples")
+    config.addinivalue_line(
+        'markers', 'xp_extension(ext): tests an Array API extension'
+    )
+    # Hypothesis
+    hypothesis_max_examples = config.getoption('--hypothesis-max-examples')
     disable_deadline = config.getoption('--hypothesis-disable-deadline')
     profile_settings = {}
     if hypothesis_max_examples is not None:
@@ -32,14 +58,49 @@ def pytest_configure(config):
     if disable_deadline is not None:
         profile_settings['deadline'] = None
     if profile_settings:
-        import hypothesis
+        settings.register_profile('xp_override', **profile_settings)
+        settings.load_profile('xp_override')
+    else:
+        settings.load_profile('xp_default')
+
+
+@lru_cache
+def xp_has_ext(ext: str) -> bool:
+    try:
+        return not isinstance(getattr(xp, ext), _UndefinedStub)
+    except AttributeError:
+        return False
 
-        hypothesis.settings.register_profile(
-            "array-api-tests-hypothesis-overridden", **profile_settings,
-        )
 
-        hypothesis.settings.load_profile("array-api-tests-hypothesis-overridden")
+xfail_ids = []
+xfails_path = Path(__file__).parent / 'xfails.txt'
+if xfails_path.exists():
+    with open(xfails_path) as f:
+        for line in f:
+            if line.startswith('array_api_tests'):
+                id_ = line.strip('\n')
+                xfail_ids.append(id_)
 
 
-settings.register_profile('array_api_tests_hypothesis_profile', deadline=800)
-settings.load_profile('array_api_tests_hypothesis_profile')
+def pytest_collection_modifyitems(config, items):
+    enabled_exts = config.getoption('--enable-extension')
+    disabled_exts = config.getoption('--disable-extension')
+    for ext in enabled_exts:
+        if ext in disabled_exts:
+            raise ValueError(f'{ext=} both enabled and disabled')
+    for item in items:
+        # enable/disable extensions
+        try:
+            ext_mark = next(m for m in item.iter_markers() if m.name == 'xp_extension')
+            ext = ext_mark.args[0]
+            if ext in disabled_exts:
+                item.add_marker(
+                    mark.skip(reason=f'{ext} disabled in --disable-extensions')
+                )
+            elif not ext in enabled_exts and not xp_has_ext(ext):
+                item.add_marker(mark.skip(reason=f'{ext} not found in array module'))
+        except StopIteration:
+            pass
+        # workflow xfail_ids
+        if item.nodeid in xfail_ids:
+            item.add_marker(mark.xfail(reason='xfails.txt'))