diff --git a/cibuildwheel/__main__.py b/cibuildwheel/__main__.py
index a770a2569..ef6f03446 100644
--- a/cibuildwheel/__main__.py
+++ b/cibuildwheel/__main__.py
@@ -12,6 +12,7 @@
 import cibuildwheel.macos
 import cibuildwheel.windows
 from cibuildwheel.environment import EnvironmentParseError, parse_environment
+from cibuildwheel.typing import PLATFORMS, PlatStr, assert_never
 from cibuildwheel.util import (
     Architecture,
     BuildOptions,
@@ -19,8 +20,8 @@
     DependencyConstraints,
     Unbuffered,
     detect_ci_provider,
-    resources_dir,
     read_python_configs,
+    resources_dir,
 )
 
 
@@ -47,6 +48,8 @@ def get_option_from_environment(option_name: str, platform: Optional[str] = None
 
 
 def main() -> None:
+    platform: PlatStr
+
     parser = argparse.ArgumentParser(
         description='Build wheels for all the platforms.',
         epilog='''
@@ -121,7 +124,7 @@ def main() -> None:
                   file=sys.stderr)
             exit(2)
 
-    if platform not in {"linux", "macos", "windows"}:
+    if platform not in PLATFORMS:
         print(f'cibuildwheel: Unsupported platform: {platform}', file=sys.stderr)
         exit(2)
 
@@ -132,8 +135,10 @@ def main() -> None:
         repair_command_default = 'auditwheel repair -w {dest_dir} {wheel}'
     elif platform == 'macos':
         repair_command_default = 'delocate-listdeps {wheel} && delocate-wheel --require-archs x86_64 -w {dest_dir} {wheel}'
-    else:
+    elif platform == 'windows':
         repair_command_default = ''
+    else:
+        assert_never(platform)
 
     build_config, skip_config = os.environ.get('CIBW_BUILD', '*'), os.environ.get('CIBW_SKIP', '')
     environment_config = get_option_from_environment('CIBW_ENVIRONMENT', platform=platform, default='')
@@ -255,6 +260,8 @@ def main() -> None:
         cibuildwheel.windows.build(build_options)
     elif platform == 'macos':
         cibuildwheel.macos.build(build_options)
+    else:
+        assert_never(platform)
 
 
 def detect_obsolete_options() -> None:
diff --git a/cibuildwheel/linux.py b/cibuildwheel/linux.py
index 1db959d3c..3d7e6a619 100644
--- a/cibuildwheel/linux.py
+++ b/cibuildwheel/linux.py
@@ -2,7 +2,7 @@
 import sys
 import textwrap
 from pathlib import Path, PurePath
-from typing import List, NamedTuple, Dict, Set
+from typing import Dict, List, NamedTuple, Set
 
 from .docker_container import DockerContainer
 from .logger import log
diff --git a/cibuildwheel/typing.py b/cibuildwheel/typing.py
index ffe8afb68..8c07d282f 100644
--- a/cibuildwheel/typing.py
+++ b/cibuildwheel/typing.py
@@ -1,6 +1,13 @@
 import os
 import subprocess
-from typing import TYPE_CHECKING, Union
+import sys
+from typing import TYPE_CHECKING, NoReturn, Set, Union
+
+if sys.version_info < (3, 8):
+    from typing_extensions import Final, Literal
+else:
+    from typing import Final, Literal
+
 
 if TYPE_CHECKING:
     PopenBytes = subprocess.Popen[bytes]
@@ -8,3 +15,11 @@
 else:
     PopenBytes = subprocess.Popen
     PathOrStr = Union[str, "os.PathLike[str]"]
+
+
+PlatStr = Literal["linux", "macos", "windows"]
+PLATFORMS: Final[Set[PlatStr]] = {"linux", "macos", "windows"}
+
+
+def assert_never(value: NoReturn) -> NoReturn:
+    assert False, f'Unhandled value: {value} ({type(value).__name__})'  # noqa: B011
diff --git a/cibuildwheel/util.py b/cibuildwheel/util.py
index 3129d9228..fc4d50a0c 100644
--- a/cibuildwheel/util.py
+++ b/cibuildwheel/util.py
@@ -3,7 +3,6 @@
 import platform as platform_module
 import re
 import ssl
-import sys
 import textwrap
 import urllib.request
 from enum import Enum
@@ -16,12 +15,7 @@
 import toml
 
 from .environment import ParsedEnvironment
-from .typing import PathOrStr
-
-if sys.version_info < (3, 8):
-    from typing_extensions import Literal
-else:
-    from typing import Literal
+from .typing import PathOrStr, PlatStr
 
 
 def prepare_command(command: str, **kwargs: PathOrStr) -> str:
@@ -158,7 +152,7 @@ def __lt__(self, other: "Architecture") -> bool:
         return self.value < other.value
 
     @staticmethod
-    def parse_config(config: str, platform: str) -> 'Set[Architecture]':
+    def parse_config(config: str, platform: PlatStr) -> 'Set[Architecture]':
         result = set()
         for arch_str in re.split(r'[\s,]+', config):
             if arch_str == 'auto':
@@ -168,7 +162,7 @@ def parse_config(config: str, platform: str) -> 'Set[Architecture]':
         return result
 
     @staticmethod
-    def auto_archs(platform: str) -> 'Set[Architecture]':
+    def auto_archs(platform: PlatStr) -> 'Set[Architecture]':
         native_architecture = Architecture(platform_module.machine())
         result = {native_architecture}
         if platform == 'linux' and native_architecture == Architecture.x86_64:
@@ -263,7 +257,7 @@ def detect_ci_provider() -> Optional[CIProvider]:
 
 
 def allowed_architectures_check(
-    name: Literal['linux', 'macos', 'windows'],
+    name: PlatStr,
     options: BuildOptions,
 ) -> None:
 
diff --git a/setup.cfg b/setup.cfg
index 3ba3b866d..2b23a5e90 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -112,6 +112,10 @@ ignore_missing_imports = True
 [mypy-bashlex.*]
 ignore_missing_imports = True
 
+# Has type stubs, but no pyproject.toml or .pyi files in the wheel.
+[mypy-toml.*]
+ignore_missing_imports = True
+
 [tool:isort]
 profile=black
 multi_line_output=3