diff --git a/cibuildwheel/linux.py b/cibuildwheel/linux.py
index 02cf6523..a8cc2e78 100644
--- a/cibuildwheel/linux.py
+++ b/cibuildwheel/linux.py
@@ -8,7 +8,7 @@ from .docker_container import DockerContainer
 from .logger import log
 from .util import (
     Architecture, BuildOptions, BuildSelector, NonPlatformWheelError,
-    get_build_verbosity_extra_flags, prepare_command,
+    allowed_architectures_check, get_build_verbosity_extra_flags, prepare_command,
 )
 from .typing import PathOrStr
 
@@ -71,6 +71,8 @@ def get_python_configurations(
 
 
 def build(options: BuildOptions) -> None:
+    allowed_architectures_check("linux", options)
+
     try:
         subprocess.check_output(['docker', '--version'])
     except Exception:
diff --git a/cibuildwheel/macos.py b/cibuildwheel/macos.py
index 82772b16..23b37bf8 100644
--- a/cibuildwheel/macos.py
+++ b/cibuildwheel/macos.py
@@ -4,15 +4,14 @@ import shutil
 import subprocess
 import sys
 import tempfile
-import textwrap
 from pathlib import Path
 from typing import Dict, List, NamedTuple, Optional, Sequence
 
 from .environment import ParsedEnvironment
 from .logger import log
-from .util import (Architecture, BuildOptions, BuildSelector, NonPlatformWheelError,
+from .util import (BuildOptions, BuildSelector, NonPlatformWheelError,
                    download, get_build_verbosity_extra_flags, get_pip_script,
-                   install_certifi_script, prepare_command)
+                   install_certifi_script, prepare_command, allowed_architectures_check)
 from .typing import PathOrStr
 
 
@@ -187,11 +186,7 @@ def setup_python(python_configuration: PythonConfiguration,
 
 
 def build(options: BuildOptions) -> None:
-    if not options.architectures <= {Architecture.x86_64}:
-        raise ValueError(textwrap.dedent(f'''
-            Invalid archs option {options.architectures}. macOS only supports x86_64 for the moment.
-            If you want to set emulation architectures on Linux, use CIBW_ARCHS_LINUX instead.
-        '''))
+    allowed_architectures_check("macos", options)
 
     temp_dir = Path(tempfile.mkdtemp(prefix='cibuildwheel'))
     built_wheel_dir = temp_dir / 'built_wheel'
diff --git a/cibuildwheel/util.py b/cibuildwheel/util.py
index 749bda77..31506a30 100644
--- a/cibuildwheel/util.py
+++ b/cibuildwheel/util.py
@@ -2,6 +2,7 @@ import os
 import platform as platform_module
 import re
 import ssl
+import sys
 import functools
 import textwrap
 import urllib.request
@@ -16,6 +17,11 @@ import certifi
 from .environment import ParsedEnvironment
 from .typing import PathOrStr
 
+if sys.version_info < (3, 8):
+    from typing_extensions import Literal
+else:
+    from typing import Literal
+
 
 def prepare_command(command: str, **kwargs: PathOrStr) -> str:
     '''
@@ -237,3 +243,33 @@ def detect_ci_provider() -> Optional[CIProvider]:
         return CIProvider.other
     else:
         return None
+
+
+PRETTY_NAMES = {'linux': 'Linux', 'macos': 'macOS', 'windows': 'Windows'}
+
+ALLOWED_ARCHITECTURES = {
+    'linux': {Architecture.x86_64, Architecture.i686, Architecture.aarch64, Architecture.ppc64le, Architecture.s390x},
+    'macos': {Architecture.x86_64},
+    'windows': {Architecture.AMD64, Architecture.x86},
+}
+
+
+def allowed_architectures_check(
+    name: Literal['linux', 'macos', 'windows'],
+    options: BuildOptions,
+) -> None:
+
+    allowed_architectures = ALLOWED_ARCHITECTURES[name]
+
+    msg = f'{PRETTY_NAMES[name]} only supports {sorted(allowed_architectures)} at the moment.'
+
+    if name != 'linux':
+        msg += ' If you want to set emulation architectures on Linux, use CIBW_ARCHS_LINUX instead.'
+
+    if not options.architectures <= allowed_architectures:
+        msg = f'Invalid archs option {options.architectures}. ' + msg
+        raise ValueError(msg)
+
+    if not options.architectures:
+        msg = 'Empty archs option set. ' + msg
+        raise ValueError(msg)
diff --git a/cibuildwheel/windows.py b/cibuildwheel/windows.py
index 09f64e1d..24d2722e 100644
--- a/cibuildwheel/windows.py
+++ b/cibuildwheel/windows.py
@@ -3,7 +3,6 @@ import shutil
 import subprocess
 import sys
 import tempfile
-import textwrap
 from pathlib import Path
 from typing import Dict, List, NamedTuple, Optional, Sequence, Set
 from zipfile import ZipFile
@@ -14,7 +13,7 @@ from .environment import ParsedEnvironment
 from .logger import log
 from .util import (Architecture, BuildOptions, BuildSelector, NonPlatformWheelError,
                    download, get_build_verbosity_extra_flags, get_pip_script,
-                   prepare_command)
+                   prepare_command, allowed_architectures_check)
 from .typing import PathOrStr
 
 IS_RUNNING_ON_AZURE = Path('C:\\hostedtoolcache').exists()
@@ -210,13 +209,7 @@ def pep_518_cp35_workaround(package_dir: Path, env: Dict[str, str]) -> None:
 
 
 def build(options: BuildOptions) -> None:
-    allowed_architectures = {Architecture.AMD64, Architecture.x86}
-    if not options.architectures <= allowed_architectures:
-        raise ValueError(textwrap.dedent(f'''
-            Invalid archs option {options.architectures}. Windows only supports
-            {sorted(allowed_architectures)}. If you want to set emulation
-            architectures on Linux, use CIBW_ARCHS_LINUX instead.
-        '''))
+    allowed_architectures_check("windows", options)
 
     temp_dir = Path(tempfile.mkdtemp(prefix='cibuildwheel'))
     built_wheel_dir = temp_dir / 'built_wheel'
diff --git a/setup.cfg b/setup.cfg
index 05d0ba2e..7f60b783 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -31,6 +31,7 @@ install_requires =
     bashlex!=0.13
     toml
     certifi
+    typing_extensions; python_version < '3.8'
 
 [options.package_data]
 cibuildwheel = resources/*