diff --git a/changelog/10875.improvement.rst b/changelog/10875.improvement.rst
new file mode 100644
index 00000000000..eeaf046350b
--- /dev/null
+++ b/changelog/10875.improvement.rst
@@ -0,0 +1 @@
+Python 3.12 support: fixed ``RuntimeError: TestResult has no addDuration method`` when running ``unittest`` tests.
diff --git a/changelog/10890.improvement.rst b/changelog/10890.improvement.rst
new file mode 100644
index 00000000000..9c367da31ef
--- /dev/null
+++ b/changelog/10890.improvement.rst
@@ -0,0 +1 @@
+Python 3.12 support: fixed ``shutil.rmtree(onerror=...)`` deprecation warning when using :fixture:`tmp_path`.
diff --git a/src/_pytest/pathlib.py b/src/_pytest/pathlib.py
index 9f9463d8862..30ed76cf89e 100644
--- a/src/_pytest/pathlib.py
+++ b/src/_pytest/pathlib.py
@@ -6,6 +6,7 @@
 import os
 import shutil
 import sys
+import types
 import uuid
 import warnings
 from enum import Enum
@@ -28,6 +29,8 @@
 from typing import Iterator
 from typing import Optional
 from typing import Set
+from typing import Tuple
+from typing import Type
 from typing import TypeVar
 from typing import Union
 
@@ -63,21 +66,33 @@ def get_lock_path(path: _AnyPurePath) -> _AnyPurePath:
     return path.joinpath(".lock")
 
 
-def on_rm_rf_error(func, path: str, exc, *, start_path: Path) -> bool:
+def on_rm_rf_error(
+    func,
+    path: str,
+    excinfo: Union[
+        BaseException,
+        Tuple[Type[BaseException], BaseException, Optional[types.TracebackType]],
+    ],
+    *,
+    start_path: Path,
+) -> bool:
     """Handle known read-only errors during rmtree.
 
     The returned value is used only by our own tests.
     """
-    exctype, excvalue = exc[:2]
+    if isinstance(excinfo, BaseException):
+        exc = excinfo
+    else:
+        exc = excinfo[1]
 
     # Another process removed the file in the middle of the "rm_rf" (xdist for example).
     # More context: https://github.com/pytest-dev/pytest/issues/5974#issuecomment-543799018
-    if isinstance(excvalue, FileNotFoundError):
+    if isinstance(exc, FileNotFoundError):
         return False
 
-    if not isinstance(excvalue, PermissionError):
+    if not isinstance(exc, PermissionError):
         warnings.warn(
-            PytestWarning(f"(rm_rf) error removing {path}\n{exctype}: {excvalue}")
+            PytestWarning(f"(rm_rf) error removing {path}\n{type(exc)}: {exc}")
         )
         return False
 
@@ -86,7 +101,7 @@ def on_rm_rf_error(func, path: str, exc, *, start_path: Path) -> bool:
             warnings.warn(
                 PytestWarning(
                     "(rm_rf) unknown function {} when removing {}:\n{}: {}".format(
-                        func, path, exctype, excvalue
+                        func, path, type(exc), exc
                     )
                 )
             )
@@ -149,7 +164,10 @@ def rm_rf(path: Path) -> None:
     are read-only."""
     path = ensure_extended_length_path(path)
     onerror = partial(on_rm_rf_error, start_path=path)
-    shutil.rmtree(str(path), onerror=onerror)
+    if sys.version_info >= (3, 12):
+        shutil.rmtree(str(path), onexc=onerror)
+    else:
+        shutil.rmtree(str(path), onerror=onerror)
 
 
 def find_prefixed(root: Path, prefix: str) -> Iterator[Path]:
diff --git a/src/_pytest/unittest.py b/src/_pytest/unittest.py
index c2df986530c..c660aa75db2 100644
--- a/src/_pytest/unittest.py
+++ b/src/_pytest/unittest.py
@@ -298,6 +298,9 @@ def addSuccess(self, testcase: "unittest.TestCase") -> None:
     def stopTest(self, testcase: "unittest.TestCase") -> None:
         pass
 
+    def addDuration(self, testcase: "unittest.TestCase", elapsed: float) -> None:
+        pass
+
     def runtest(self) -> None:
         from _pytest.debugging import maybe_wrap_pytest_function_for_tracing
 
diff --git a/testing/test_tmpdir.py b/testing/test_tmpdir.py
index fcb0775dd5f..110a68b278d 100644
--- a/testing/test_tmpdir.py
+++ b/testing/test_tmpdir.py
@@ -512,20 +512,20 @@ def test_on_rm_rf_error(self, tmp_path: Path) -> None:
 
         # unknown exception
         with pytest.warns(pytest.PytestWarning):
-            exc_info1 = (None, RuntimeError(), None)
+            exc_info1 = (RuntimeError, RuntimeError(), None)
             on_rm_rf_error(os.unlink, str(fn), exc_info1, start_path=tmp_path)
             assert fn.is_file()
 
         # we ignore FileNotFoundError
-        exc_info2 = (None, FileNotFoundError(), None)
+        exc_info2 = (FileNotFoundError, FileNotFoundError(), None)
         assert not on_rm_rf_error(None, str(fn), exc_info2, start_path=tmp_path)
 
         # unknown function
         with pytest.warns(
             pytest.PytestWarning,
-            match=r"^\(rm_rf\) unknown function None when removing .*foo.txt:\nNone: ",
+            match=r"^\(rm_rf\) unknown function None when removing .*foo.txt:\n<class 'PermissionError'>: ",
         ):
-            exc_info3 = (None, PermissionError(), None)
+            exc_info3 = (PermissionError, PermissionError(), None)
             on_rm_rf_error(None, str(fn), exc_info3, start_path=tmp_path)
             assert fn.is_file()
 
@@ -533,12 +533,12 @@ def test_on_rm_rf_error(self, tmp_path: Path) -> None:
         with warnings.catch_warnings():
             warnings.simplefilter("ignore")
             with pytest.warns(None) as warninfo:  # type: ignore[call-overload]
-                exc_info4 = (None, PermissionError(), None)
+                exc_info4 = PermissionError()
                 on_rm_rf_error(os.open, str(fn), exc_info4, start_path=tmp_path)
                 assert fn.is_file()
             assert not [x.message for x in warninfo]
 
-        exc_info5 = (None, PermissionError(), None)
+        exc_info5 = PermissionError()
         on_rm_rf_error(os.unlink, str(fn), exc_info5, start_path=tmp_path)
         assert not fn.is_file()