diff --git a/src/spox/_adapt.py b/src/spox/_adapt.py
index 8877e40..42aad5b 100644
--- a/src/spox/_adapt.py
+++ b/src/spox/_adapt.py
@@ -1,8 +1,9 @@
 # Copyright (c) QuantCo 2023-2024
 # SPDX-License-Identifier: BSD-3-Clause
 
+from __future__ import annotations
+
 import warnings
-from typing import Optional
 
 import onnx
 import onnx.version_converter
@@ -22,7 +23,7 @@ def adapt_node(
     source_version: int,
     target_version: int,
     var_names: dict[_VarInfo, str],
-) -> Optional[list[onnx.NodeProto]]:
+) -> list[onnx.NodeProto] | None:
     if source_version == target_version:
         return None
 
@@ -93,7 +94,7 @@ def adapt_best_effort(
     opsets: dict[str, int],
     var_names: dict[_VarInfo, str],
     node_names: dict[Node, str],
-) -> Optional[list[onnx.NodeProto]]:
+) -> list[onnx.NodeProto] | None:
     if isinstance(node, _Inline):
         return adapt_inline(
             node,
diff --git a/src/spox/_fields.py b/src/spox/_fields.py
index 07c09ed..5cb77be 100644
--- a/src/spox/_fields.py
+++ b/src/spox/_fields.py
@@ -10,9 +10,9 @@
 from dataclasses import Field, dataclass
 from typing import Optional, get_type_hints
 
+from . import _type_system
 from ._attributes import Attr
 from ._exceptions import InferenceWarning
-from ._type_system import Optional as tOptional
 from ._value_prop import PropDict, PropValue
 from ._var import Var, _VarInfo
 
@@ -160,7 +160,10 @@ def _create_var(key: str, var_info: _VarInfo) -> Var:
             if var_info.type is None or key not in prop_values:
                 return ret
 
-            if not isinstance(var_info.type, tOptional) and prop_values[key] is None:
+            if (
+                not isinstance(var_info.type, _type_system.Optional)
+                and prop_values[key] is None
+            ):
                 return ret
 
             prop = PropValue(var_info.type, prop_values[key])
diff --git a/src/spox/_public.py b/src/spox/_public.py
index e12240e..369a67f 100644
--- a/src/spox/_public.py
+++ b/src/spox/_public.py
@@ -3,10 +3,12 @@
 
 """Module implementing the main public interface functions in Spox."""
 
+from __future__ import annotations
+
 import contextlib
 import itertools
 from collections.abc import Iterator
-from typing import Optional, Protocol
+from typing import Protocol
 
 import numpy as np
 import onnx
@@ -51,8 +53,8 @@ def _temporary_renames(**kwargs: Var) -> Iterator[None]:
     # The build code can't really special-case variable names that are
     # not just ``Var._name``.  So we set names here and reset them
     # afterwards.
-    name: Optional[str]
-    pre: dict[Var, Optional[str]] = {}
+    name: str | None
+    pre: dict[Var, str | None] = {}
     try:
         for name, arg in kwargs.items():
             pre[arg] = arg._var_info._name
diff --git a/src/spox/_schemas.py b/src/spox/_schemas.py
index 7486dcc..4eb51c2 100644
--- a/src/spox/_schemas.py
+++ b/src/spox/_schemas.py
@@ -3,9 +3,11 @@
 
 """Exposes information related to reference ONNX operator schemas, used by StandardOpNode."""
 
+from __future__ import annotations
+
 import itertools
 from collections.abc import Iterable
-from typing import Any, Callable, Optional, Protocol, TypeVar
+from typing import Any, Callable, Protocol, TypeVar
 
 from onnx.defs import OpSchema, get_all_schemas_with_history
 
@@ -30,8 +32,8 @@ def _key_groups(
 
 
 def _current_schema(
-    schemas: Iterable[OpSchema], version: Optional[int] = None
-) -> Optional[OpSchema]:
+    schemas: Iterable[OpSchema], version: int | None = None
+) -> OpSchema | None:
     """
     Find the schema for the current ``version`` from the list (the latest existing version).
     If ``version`` is None (or left to default), the newest of the schemas is returned.
diff --git a/src/spox/_traverse.py b/src/spox/_traverse.py
index 6b64189..4a32775 100644
--- a/src/spox/_traverse.py
+++ b/src/spox/_traverse.py
@@ -1,8 +1,10 @@
 # Copyright (c) QuantCo 2023-2024
 # SPDX-License-Identifier: BSD-3-Clause
 
+from __future__ import annotations
+
 from collections.abc import Iterable, Iterator
-from typing import Callable, Optional, TypeVar
+from typing import Callable, TypeVar
 
 V = TypeVar("V")
 
@@ -10,7 +12,7 @@
 def iterative_dfs(
     sources: Iterable[V],
     adj: Callable[[V], Iterable[V]],
-    post_callback: Optional[Callable[[V], None]] = None,
+    post_callback: Callable[[V], None] | None = None,
     raise_on_cycle: bool = True,
 ) -> list[V]:
     """
diff --git a/src/spox/_utils.py b/src/spox/_utils.py
index af6ed1a..7b00de4 100644
--- a/src/spox/_utils.py
+++ b/src/spox/_utils.py
@@ -1,7 +1,7 @@
 # Copyright (c) QuantCo 2023-2024
 # SPDX-License-Identifier: BSD-3-Clause
 
-from typing import Optional
+from __future__ import annotations
 
 import numpy as np
 import numpy.typing as npt
@@ -42,7 +42,7 @@ def dtype_to_tensor_type(dtype_like: npt.DTypeLike) -> int:
         raise TypeError(err_msg)
 
 
-def from_array(arr: np.ndarray, name: Optional[str] = None) -> TensorProto:
+def from_array(arr: np.ndarray, name: str | None = None) -> TensorProto:
     """Convert the given ``numpy.array`` into an ``onnx.TensorProto``.
 
     As it may be useful to name the TensorProto (e.g. in