diff --git a/changes/2714.misc.rst b/changes/2714.misc.rst
new file mode 100644
index 0000000000..9ab55089d2
--- /dev/null
+++ b/changes/2714.misc.rst
@@ -0,0 +1 @@
+Make warning filters in the tests more specific, so warnings emitted by tests added in the future are more likely to be caught instead of ignored.
diff --git a/pyproject.toml b/pyproject.toml
index d862cce0ac..1ee5678f82 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -397,12 +397,18 @@ addopts = [
     "--durations=10", "-ra", "--strict-config", "--strict-markers",
 ]
 filterwarnings = [
-    "error:::zarr.*",
-    "ignore:PY_SSIZE_T_CLEAN will be required.*:DeprecationWarning",
-    "ignore:The loop argument is deprecated since Python 3.8.*:DeprecationWarning",
-    "ignore:Creating a zarr.buffer.gpu.*:UserWarning",
-    "ignore:Duplicate name:UserWarning",  # from ZipFile
-    "ignore:.*is currently not part in the Zarr format 3 specification.*:UserWarning",
+    "error",
+    # TODO: explicitly filter or catch the warnings below where we expect them to be emitted in the tests
+    "ignore:Consolidated metadata is currently not part in the Zarr format 3 specification.*:UserWarning",
+    "ignore:Creating a zarr.buffer.gpu.Buffer with an array that does not support the __cuda_array_interface__.*:UserWarning",
+    "ignore:Automatic shard shape inference is experimental and may change without notice.*:UserWarning",
+    "ignore:The codec .* is currently not part in the Zarr format 3 specification.*:UserWarning",
+    "ignore:The dtype .* is currently not part in the Zarr format 3 specification.*:UserWarning",
+    "ignore:Use zarr.create_array instead.:DeprecationWarning",
+    "ignore:Duplicate name.*:UserWarning",
+    "ignore:The `compressor` argument is deprecated. Use `compressors` instead.:UserWarning",
+    "ignore:Numcodecs codecs are not in the Zarr version 3 specification and may not be supported by other zarr implementations.:UserWarning",
+    "ignore:Unclosed client session <aiohttp.client.ClientSession.*:ResourceWarning"
 ]
 markers = [
     "gpu: mark a test as requiring CuPy and GPU",
diff --git a/tests/test_array.py b/tests/test_array.py
index efcf8a6bf9..3751d5409e 100644
--- a/tests/test_array.py
+++ b/tests/test_array.py
@@ -1417,9 +1417,8 @@ def test_multiprocessing(store: Store, method: Literal["fork", "spawn", "forkser
     data = np.arange(100)
     arr = zarr.create_array(store=store, data=data)
     ctx = mp.get_context(method)
-    pool = ctx.Pool()
-
-    results = pool.starmap(_index_array, [(arr, slice(len(data)))])
+    with ctx.Pool() as pool:
+        results = pool.starmap(_index_array, [(arr, slice(len(data)))])
     assert all(np.array_equal(r, data) for r in results)
 
 
diff --git a/tests/test_store/test_fsspec.py b/tests/test_store/test_fsspec.py
index 2e9620f29d..08cf2f286d 100644
--- a/tests/test_store/test_fsspec.py
+++ b/tests/test_store/test_fsspec.py
@@ -2,6 +2,7 @@
 
 import json
 import os
+import re
 from typing import TYPE_CHECKING
 
 import pytest
@@ -19,6 +20,17 @@
 
     import botocore.client
 
+# Warning filter due to https://github.com/boto/boto3/issues/3889
+pytestmark = [
+    pytest.mark.filterwarnings(
+        re.escape("ignore:datetime.datetime.utcnow() is deprecated:DeprecationWarning")
+    ),
+    # TODO: fix these warnings
+    pytest.mark.filterwarnings("ignore:Unclosed client session:ResourceWarning"),
+    pytest.mark.filterwarnings(
+        "ignore:coroutine 'ClientCreatorContext.__aexit__' was never awaited:RuntimeWarning"
+    ),
+]
 
 fsspec = pytest.importorskip("fsspec")
 s3fs = pytest.importorskip("s3fs")
diff --git a/tests/test_store/test_memory.py b/tests/test_store/test_memory.py
index f00d75a8f0..e520c7d054 100644
--- a/tests/test_store/test_memory.py
+++ b/tests/test_store/test_memory.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import re
 from typing import TYPE_CHECKING
 
 import numpy as np
@@ -15,6 +16,10 @@
     from zarr.core.common import ZarrFormat
 
 
+# TODO: work out where this warning is coming from and fix it
+@pytest.mark.filterwarnings(
+    re.escape("ignore:coroutine 'ClientCreatorContext.__aexit__' was never awaited")
+)
 class TestMemoryStore(StoreTests[MemoryStore, cpu.Buffer]):
     store_cls = MemoryStore
     buffer_cls = cpu.Buffer
@@ -73,6 +78,8 @@ async def test_deterministic_size(
         np.testing.assert_array_equal(a[3:], 0)
 
 
+# TODO: fix this warning
+@pytest.mark.filterwarnings("ignore:Unclosed client session:ResourceWarning")
 @gpu_test
 class TestGpuMemoryStore(StoreTests[GpuMemoryStore, gpu.Buffer]):
     store_cls = GpuMemoryStore
diff --git a/tests/test_store/test_stateful.py b/tests/test_store/test_stateful.py
index 63df814ac9..a17d7a55be 100644
--- a/tests/test_store/test_stateful.py
+++ b/tests/test_store/test_stateful.py
@@ -8,7 +8,11 @@
 from zarr.storage import LocalStore, ZipStore
 from zarr.testing.stateful import ZarrHierarchyStateMachine, ZarrStoreStateMachine
 
-pytestmark = pytest.mark.slow_hypothesis
+pytestmark = [
+    pytest.mark.slow_hypothesis,
+    # TODO: work out where this warning is coming from and fix
+    pytest.mark.filterwarnings("ignore:Unclosed client session:ResourceWarning"),
+]
 
 
 def test_zarr_hierarchy(sync_store: Store):
diff --git a/tests/test_store/test_wrapper.py b/tests/test_store/test_wrapper.py
index 7e933548b3..c6edd4f4dd 100644
--- a/tests/test_store/test_wrapper.py
+++ b/tests/test_store/test_wrapper.py
@@ -15,6 +15,10 @@
     from zarr.core.buffer.core import BufferPrototype
 
 
+# TODO: fix this warning
+@pytest.mark.filterwarnings(
+    "ignore:coroutine 'ClientCreatorContext.__aexit__' was never awaited:RuntimeWarning"
+)
 class TestWrapperStore(StoreTests[WrapperStore, Buffer]):
     store_cls = WrapperStore
     buffer_cls = Buffer
@@ -72,6 +76,10 @@ def test_is_open_setter_raises(self, store: WrapperStore) -> None:
             store._is_open = True
 
 
+# TODO: work out where warning is coming from and fix
+@pytest.mark.filterwarnings(
+    "ignore:coroutine 'ClientCreatorContext.__aexit__' was never awaited:RuntimeWarning"
+)
 @pytest.mark.parametrize("store", ["local", "memory", "zip"], indirect=True)
 async def test_wrapped_set(store: Store, capsys: pytest.CaptureFixture[str]) -> None:
     # define a class that prints when it sets
@@ -89,6 +97,7 @@ async def set(self, key: str, value: Buffer) -> None:
     assert await store_wrapped.get(key, buffer_prototype) == value
 
 
+@pytest.mark.filterwarnings("ignore:Unclosed client session:ResourceWarning")
 @pytest.mark.parametrize("store", ["local", "memory", "zip"], indirect=True)
 async def test_wrapped_get(store: Store, capsys: pytest.CaptureFixture[str]) -> None:
     # define a class that prints when it sets
diff --git a/tests/test_store/test_zip.py b/tests/test_store/test_zip.py
index 839656108b..0237258ab1 100644
--- a/tests/test_store/test_zip.py
+++ b/tests/test_store/test_zip.py
@@ -19,6 +19,14 @@
     from typing import Any
 
 
+# TODO: work out where this is coming from and fix
+pytestmark = [
+    pytest.mark.filterwarnings(
+        "ignore:coroutine method 'aclose' of 'ZipStore.list' was never awaited:RuntimeWarning"
+    )
+]
+
+
 class TestZipStore(StoreTests[ZipStore, cpu.Buffer]):
     store_cls = ZipStore
     buffer_cls = cpu.Buffer
@@ -66,6 +74,8 @@ def test_store_supports_partial_writes(self, store: ZipStore) -> None:
     def test_store_supports_listing(self, store: ZipStore) -> None:
         assert store.supports_listing
 
+    # TODO: fix this warning
+    @pytest.mark.filterwarnings("ignore:Unclosed client session:ResourceWarning")
     def test_api_integration(self, store: ZipStore) -> None:
         root = zarr.open_group(store=store, mode="a")
 
diff --git a/tests/test_sync.py b/tests/test_sync.py
index e0002fc5a7..13b475f8da 100644
--- a/tests/test_sync.py
+++ b/tests/test_sync.py
@@ -90,6 +90,7 @@ def test_sync_raises_if_loop_is_closed() -> None:
     foo.assert_not_awaited()
 
 
+@pytest.mark.filterwarnings("ignore:Unclosed client session:ResourceWarning")
 @pytest.mark.filterwarnings("ignore:coroutine.*was never awaited")
 def test_sync_raises_if_calling_sync_from_within_a_running_loop(
     sync_loop: asyncio.AbstractEventLoop | None,