diff --git a/.azure-pipelines.yml b/.azure-pipelines.yml
index 87974a34d..90b32de88 100644
--- a/.azure-pipelines.yml
+++ b/.azure-pipelines.yml
@@ -4,8 +4,7 @@ trigger:
 
 variables:
   RUN_COVERAGE: no
-  # TODO: remove paths after moving tests to test dir: https://github.com/scverse/anndata/issues/1451
-  PYTEST_ADDOPTS: --color=yes --junitxml=test-data/test-results.xml anndata ./src/anndata/tests ./docs/concatenation.rst
+  PYTEST_ADDOPTS: --color=yes --junitxml=test-data/test-results.xml
   DEPENDENCIES_VERSION: "latest" # |"pre-release" | "minimum-version"
   TEST_TYPE: "standard" # | "coverage"
 
@@ -85,16 +84,6 @@ jobs:
         displayName: "PyTest (treat warnings as errors)"
         condition: eq(variables['TEST_TYPE'], 'strict-warning')
 
-      # TODO: remove: https://github.com/scverse/anndata/issues/1451
-      - task: PythonScript@0
-        inputs:
-          scriptSource: inline
-          script: |
-            import sys, xml.etree.ElementTree as ET
-            results = ET.parse("./test-data/test-results.xml").findall("./*/*")
-            sys.exit(0 if len(results) > 3000 else f"Error: only {len(results)} tests run")
-        displayName: "Check if enough tests ran"
-
       - task: PublishCodeCoverageResults@2
         inputs:
           codeCoverageTool: Cobertura
diff --git a/.codecov.yml b/.codecov.yml
index 68cc92f2d..48f7a5e06 100644
--- a/.codecov.yml
+++ b/.codecov.yml
@@ -1,16 +1,16 @@
 # Based on pydata/xarray
 codecov:
-  require_ci_to_pass: no
+  require_ci_to_pass: false
 
 coverage:
   status:
     project:
       default:
-        # Require 1% coverage, i.e., always succeed
-        target: 1
+        # Require 80% coverage
+        target: 80
     changes: false
 
 comment:
   layout: "diff, flags, files"
   behavior: once
-  require_base: no
+  require_base: false
diff --git a/conftest.py b/conftest.py
index 578bc71d9..8e7216015 100644
--- a/conftest.py
+++ b/conftest.py
@@ -18,6 +18,17 @@
     from pathlib import Path
 
 
+# TODO: Should be done in pyproject.toml eventually
+# See https://github.com/pytest-dev/pytest-cov/issues/437
+def pytest_configure(config: pytest.Config) -> None:
+    config.addinivalue_line(
+        "filterwarnings", "ignore::anndata._warnings.OldFormatWarning"
+    )
+    config.addinivalue_line(
+        "filterwarnings", "ignore::anndata._warnings.ExperimentalFeatureWarning"
+    )
+
+
 @pytest.fixture(autouse=True)
 def _suppress_env_for_doctests(request: pytest.FixtureRequest) -> None:
     if isinstance(request.node, pytest.DoctestItem):
diff --git a/pyproject.toml b/pyproject.toml
index 183ffdcd8..f27cc4fd7 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -83,7 +83,7 @@ doc = [
 ]
 test = [
     "loompy>=3.0.5",
-    "pytest>=8.0",
+    "pytest>=8.2",
     "pytest-cov>=2.10",
     "zarr",
     "matplotlib",
@@ -101,12 +101,6 @@ test = [
 ]
 gpu = ["cupy"]
 
-[tool.hatch.build]
-exclude = [
-    "src/anndata/tests/conftest.py",
-    "src/anndata/tests/test_*.py",
-    "src/anndata/tests/data",
-]
 [tool.hatch.version]
 source = "vcs"
 [tool.hatch.build.hooks.vcs]
@@ -125,7 +119,7 @@ exclude_also = [
 
 [tool.pytest.ini_options]
 addopts = [
-    # "--import-mode=importlib", # TODO: enable: https://github.com/scverse/anndata/issues/1451
+    "--import-mode=importlib",
     "--strict-markers",
     "--doctest-modules",
     "--pyargs",
@@ -133,10 +127,8 @@ addopts = [
     "--ignore=anndata/readwrite.py", # deprecated
 ]
 filterwarnings = [
-    'ignore:Support for Awkward Arrays is currently experimental',
-    'ignore:Outer joins on awkward\.Arrays',
-    # TODO: replace both lines above with this one once we figured out how prevent ImportPathMismatchError
-    # 'ignore::anndata._warnings.ExperimentalFeatureWarning',
+    # all `ignore::anndata.*` entries are in `conftest.py`
+    # See: https://github.com/pytest-dev/pytest-cov/issues/437
 ]
 # When `--strict-warnings` is used, all warnings are treated as errors, except those:
 filterwarnings_when_strict = [
@@ -148,7 +140,8 @@ filterwarnings_when_strict = [
 ]
 python_files = "test_*.py"
 testpaths = [
-    "anndata", # docstrings and unit tests (module name due to --pyargs)
+    "anndata", # docstrings (module name due to --pyargs)
+    "./tests", # unit tests
     "./docs/concatenation.rst", # further doctests
 ]
 # For some reason this effects how logging is shown when tests are run
@@ -182,7 +175,7 @@ ignore = [
 ]
 [tool.ruff.lint.per-file-ignores]
 # E721 comparing types, but we specifically are checking that we aren't getting subtypes (views)
-"src/anndata/tests/test_readwrite.py" = ["E721"]
+"tests/test_readwrite.py" = ["E721"]
 [tool.ruff.lint.isort]
 known-first-party = ["anndata"]
 required-imports = ["from __future__ import annotations"]
diff --git a/src/anndata/tests/conftest.py b/src/anndata/tests/conftest.py
deleted file mode 100644
index e45bf708b..000000000
--- a/src/anndata/tests/conftest.py
+++ /dev/null
@@ -1,19 +0,0 @@
-from __future__ import annotations
-
-import warnings
-
-import pytest
-
-import anndata
-from anndata.tests.helpers import subset_func  # noqa: F401
-
-# TODO: Should be done in pyproject.toml, see anndata/conftest.py
-warnings.filterwarnings("ignore", category=anndata.OldFormatWarning)
-
-# TODO: remove once we extricated test utils and tests
-collect_ignore = ["helpers.py"]
-
-
-@pytest.fixture
-def backing_h5ad(tmp_path):
-    return tmp_path / "test.h5ad"
diff --git a/tests/conftest.py b/tests/conftest.py
new file mode 100644
index 000000000..22ec4b6bd
--- /dev/null
+++ b/tests/conftest.py
@@ -0,0 +1,10 @@
+from __future__ import annotations
+
+import pytest
+
+from anndata.tests.helpers import subset_func  # noqa: F401
+
+
+@pytest.fixture
+def backing_h5ad(tmp_path):
+    return tmp_path / "test.h5ad"
diff --git a/src/anndata/tests/adata-comments.tsv b/tests/data/adata-comments.tsv
similarity index 100%
rename from src/anndata/tests/adata-comments.tsv
rename to tests/data/adata-comments.tsv
diff --git a/src/anndata/tests/adata.csv b/tests/data/adata.csv
similarity index 100%
rename from src/anndata/tests/adata.csv
rename to tests/data/adata.csv
diff --git a/src/anndata/tests/data/archives/readme.md b/tests/data/archives/readme.md
similarity index 100%
rename from src/anndata/tests/data/archives/readme.md
rename to tests/data/archives/readme.md
diff --git a/src/anndata/tests/data/archives/v0.7.0/adata.h5ad b/tests/data/archives/v0.7.0/adata.h5ad
similarity index 100%
rename from src/anndata/tests/data/archives/v0.7.0/adata.h5ad
rename to tests/data/archives/v0.7.0/adata.h5ad
diff --git a/src/anndata/tests/data/archives/v0.7.0/adata.zarr.zip b/tests/data/archives/v0.7.0/adata.zarr.zip
similarity index 100%
rename from src/anndata/tests/data/archives/v0.7.0/adata.zarr.zip
rename to tests/data/archives/v0.7.0/adata.zarr.zip
diff --git a/src/anndata/tests/data/archives/v0.7.8/adata.h5ad b/tests/data/archives/v0.7.8/adata.h5ad
similarity index 100%
rename from src/anndata/tests/data/archives/v0.7.8/adata.h5ad
rename to tests/data/archives/v0.7.8/adata.h5ad
diff --git a/src/anndata/tests/data/archives/v0.7.8/adata.zarr.zip b/tests/data/archives/v0.7.8/adata.zarr.zip
similarity index 100%
rename from src/anndata/tests/data/archives/v0.7.8/adata.zarr.zip
rename to tests/data/archives/v0.7.8/adata.zarr.zip
diff --git a/src/anndata/tests/data/excel.xlsx b/tests/data/excel.xlsx
similarity index 100%
rename from src/anndata/tests/data/excel.xlsx
rename to tests/data/excel.xlsx
diff --git a/src/anndata/tests/data/umi_tools.tsv.gz b/tests/data/umi_tools.tsv.gz
similarity index 100%
rename from src/anndata/tests/data/umi_tools.tsv.gz
rename to tests/data/umi_tools.tsv.gz
diff --git a/src/anndata/tests/test_anncollection.py b/tests/test_anncollection.py
similarity index 100%
rename from src/anndata/tests/test_anncollection.py
rename to tests/test_anncollection.py
diff --git a/src/anndata/tests/test_annot.py b/tests/test_annot.py
similarity index 100%
rename from src/anndata/tests/test_annot.py
rename to tests/test_annot.py
diff --git a/src/anndata/tests/test_awkward.py b/tests/test_awkward.py
similarity index 100%
rename from src/anndata/tests/test_awkward.py
rename to tests/test_awkward.py
diff --git a/src/anndata/tests/test_backed_sparse.py b/tests/test_backed_sparse.py
similarity index 100%
rename from src/anndata/tests/test_backed_sparse.py
rename to tests/test_backed_sparse.py
diff --git a/src/anndata/tests/test_base.py b/tests/test_base.py
similarity index 100%
rename from src/anndata/tests/test_base.py
rename to tests/test_base.py
diff --git a/src/anndata/tests/test_concatenate.py b/tests/test_concatenate.py
similarity index 100%
rename from src/anndata/tests/test_concatenate.py
rename to tests/test_concatenate.py
diff --git a/src/anndata/tests/test_concatenate_disk.py b/tests/test_concatenate_disk.py
similarity index 100%
rename from src/anndata/tests/test_concatenate_disk.py
rename to tests/test_concatenate_disk.py
diff --git a/src/anndata/tests/test_dask.py b/tests/test_dask.py
similarity index 100%
rename from src/anndata/tests/test_dask.py
rename to tests/test_dask.py
diff --git a/src/anndata/tests/test_dask_view_mem.py b/tests/test_dask_view_mem.py
similarity index 100%
rename from src/anndata/tests/test_dask_view_mem.py
rename to tests/test_dask_view_mem.py
diff --git a/src/anndata/tests/test_deprecations.py b/tests/test_deprecations.py
similarity index 100%
rename from src/anndata/tests/test_deprecations.py
rename to tests/test_deprecations.py
diff --git a/src/anndata/tests/test_get_vector.py b/tests/test_get_vector.py
similarity index 100%
rename from src/anndata/tests/test_get_vector.py
rename to tests/test_get_vector.py
diff --git a/src/anndata/tests/test_gpu.py b/tests/test_gpu.py
similarity index 100%
rename from src/anndata/tests/test_gpu.py
rename to tests/test_gpu.py
diff --git a/src/anndata/tests/test_hdf5_backing.py b/tests/test_hdf5_backing.py
similarity index 100%
rename from src/anndata/tests/test_hdf5_backing.py
rename to tests/test_hdf5_backing.py
diff --git a/src/anndata/tests/test_helpers.py b/tests/test_helpers.py
similarity index 100%
rename from src/anndata/tests/test_helpers.py
rename to tests/test_helpers.py
diff --git a/src/anndata/tests/test_inplace_subset.py b/tests/test_inplace_subset.py
similarity index 100%
rename from src/anndata/tests/test_inplace_subset.py
rename to tests/test_inplace_subset.py
diff --git a/src/anndata/tests/test_io_backwards_compat.py b/tests/test_io_backwards_compat.py
similarity index 100%
rename from src/anndata/tests/test_io_backwards_compat.py
rename to tests/test_io_backwards_compat.py
diff --git a/src/anndata/tests/test_io_conversion.py b/tests/test_io_conversion.py
similarity index 100%
rename from src/anndata/tests/test_io_conversion.py
rename to tests/test_io_conversion.py
diff --git a/src/anndata/tests/test_io_dispatched.py b/tests/test_io_dispatched.py
similarity index 100%
rename from src/anndata/tests/test_io_dispatched.py
rename to tests/test_io_dispatched.py
diff --git a/src/anndata/tests/test_io_elementwise.py b/tests/test_io_elementwise.py
similarity index 100%
rename from src/anndata/tests/test_io_elementwise.py
rename to tests/test_io_elementwise.py
diff --git a/src/anndata/tests/test_io_partial.py b/tests/test_io_partial.py
similarity index 100%
rename from src/anndata/tests/test_io_partial.py
rename to tests/test_io_partial.py
diff --git a/src/anndata/tests/test_io_utils.py b/tests/test_io_utils.py
similarity index 100%
rename from src/anndata/tests/test_io_utils.py
rename to tests/test_io_utils.py
diff --git a/src/anndata/tests/test_io_warnings.py b/tests/test_io_warnings.py
similarity index 100%
rename from src/anndata/tests/test_io_warnings.py
rename to tests/test_io_warnings.py
diff --git a/src/anndata/tests/test_layers.py b/tests/test_layers.py
similarity index 100%
rename from src/anndata/tests/test_layers.py
rename to tests/test_layers.py
diff --git a/src/anndata/tests/test_obsmvarm.py b/tests/test_obsmvarm.py
similarity index 100%
rename from src/anndata/tests/test_obsmvarm.py
rename to tests/test_obsmvarm.py
diff --git a/src/anndata/tests/test_obspvarp.py b/tests/test_obspvarp.py
similarity index 100%
rename from src/anndata/tests/test_obspvarp.py
rename to tests/test_obspvarp.py
diff --git a/src/anndata/tests/test_raw.py b/tests/test_raw.py
similarity index 100%
rename from src/anndata/tests/test_raw.py
rename to tests/test_raw.py
diff --git a/src/anndata/tests/test_readwrite.py b/tests/test_readwrite.py
similarity index 99%
rename from src/anndata/tests/test_readwrite.py
rename to tests/test_readwrite.py
index 0c87eae6e..49a0a48fb 100644
--- a/src/anndata/tests/test_readwrite.py
+++ b/tests/test_readwrite.py
@@ -467,21 +467,21 @@ def test_readloom_deprecations(tmp_path):
 
 
 def test_read_csv():
-    adata = ad.read_csv(HERE / "adata.csv")
+    adata = ad.read_csv(HERE / "data" / "adata.csv")
     assert adata.obs_names.tolist() == ["r1", "r2", "r3"]
     assert adata.var_names.tolist() == ["c1", "c2"]
     assert adata.X.tolist() == X_list
 
 
 def test_read_tsv_strpath():
-    adata = ad.read_text(str(HERE / "adata-comments.tsv"), "\t")
+    adata = ad.read_text(str(HERE / "data" / "adata-comments.tsv"), "\t")
     assert adata.obs_names.tolist() == ["r1", "r2", "r3"]
     assert adata.var_names.tolist() == ["c1", "c2"]
     assert adata.X.tolist() == X_list
 
 
 def test_read_tsv_iter():
-    with (HERE / "adata-comments.tsv").open() as f:
+    with (HERE / "data" / "adata-comments.tsv").open() as f:
         adata = ad.read_text(f, "\t")
     assert adata.obs_names.tolist() == ["r1", "r2", "r3"]
     assert adata.var_names.tolist() == ["c1", "c2"]
diff --git a/src/anndata/tests/test_repr.py b/tests/test_repr.py
similarity index 100%
rename from src/anndata/tests/test_repr.py
rename to tests/test_repr.py
diff --git a/src/anndata/tests/test_structured_arrays.py b/tests/test_structured_arrays.py
similarity index 100%
rename from src/anndata/tests/test_structured_arrays.py
rename to tests/test_structured_arrays.py
diff --git a/src/anndata/tests/test_transpose.py b/tests/test_transpose.py
similarity index 100%
rename from src/anndata/tests/test_transpose.py
rename to tests/test_transpose.py
diff --git a/src/anndata/tests/test_uns.py b/tests/test_uns.py
similarity index 100%
rename from src/anndata/tests/test_uns.py
rename to tests/test_uns.py
diff --git a/src/anndata/tests/test_utils.py b/tests/test_utils.py
similarity index 100%
rename from src/anndata/tests/test_utils.py
rename to tests/test_utils.py
diff --git a/src/anndata/tests/test_views.py b/tests/test_views.py
similarity index 100%
rename from src/anndata/tests/test_views.py
rename to tests/test_views.py
diff --git a/src/anndata/tests/test_x.py b/tests/test_x.py
similarity index 100%
rename from src/anndata/tests/test_x.py
rename to tests/test_x.py