diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8263f5df..4f326d81 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,12 @@ All versions prior to 0.0.9 are untracked.
 
 ## [Unreleased]
 
+### Changed
+
+* Improved error messaging when a requirements input or indirect dependency
+  has an invalid (non-PEP 440) requirements specifier
+  ([#507](https://github.com/pypa/pip-audit/pull/507))
+
 ## [2.4.15]
 
 ### Fixed
diff --git a/pip_audit/_dependency_source/__init__.py b/pip_audit/_dependency_source/__init__.py
index 97f5db2c..32fa4818 100644
--- a/pip_audit/_dependency_source/__init__.py
+++ b/pip_audit/_dependency_source/__init__.py
@@ -10,6 +10,7 @@
     DependencySourceError,
     HashMismatchError,
     HashMissingError,
+    InvalidRequirementSpecifier,
     RequirementHashes,
     UnsupportedHashAlgorithm,
 )
@@ -27,6 +28,7 @@
     "DependencySourceError",
     "HashMismatchError",
     "HashMissingError",
+    "InvalidRequirementSpecifier",
     "PipSource",
     "PipSourceError",
     "PyProjectSource",
diff --git a/pip_audit/_dependency_source/interface.py b/pip_audit/_dependency_source/interface.py
index 337f83e5..b4efa550 100644
--- a/pip_audit/_dependency_source/interface.py
+++ b/pip_audit/_dependency_source/interface.py
@@ -86,6 +86,13 @@ class UnsupportedHashAlgorithm(Exception):
     pass
 
 
+class InvalidRequirementSpecifier(DependencySourceError):
+    """
+    A `DependencySourceError` specialized for the case of a non-PEP 440 requirements
+    specifier.
+    """
+
+
 class RequirementHashes:
     """
     Represents the hashes contained within a requirements file.
diff --git a/pip_audit/_dependency_source/requirement.py b/pip_audit/_dependency_source/requirement.py
index 97cf60c8..a0b19149 100644
--- a/pip_audit/_dependency_source/requirement.py
+++ b/pip_audit/_dependency_source/requirement.py
@@ -25,6 +25,7 @@
     DependencyResolverError,
     DependencySource,
     DependencySourceError,
+    InvalidRequirementSpecifier,
     RequirementHashes,
 )
 from pip_audit._fix import ResolvedFixVersion
@@ -89,10 +90,11 @@ def collect(self) -> Iterator[Dependency]:
         for filename in self._filenames:
             try:
                 rf = RequirementsFile.from_file(filename)
-                if rf.invalid_lines:
-                    raise RequirementSourceError(
-                        f"requirement file {filename} contains invalid lines: "
-                        f"{str(rf.invalid_lines)}"
+                if len(rf.invalid_lines) > 0:
+                    invalid = rf.invalid_lines[0]
+                    raise InvalidRequirementSpecifier(
+                        f"requirement file {filename} contains invalid specifier at "
+                        f"line {invalid.line_number}: {invalid.error_message}"
                     )
 
                 reqs: list[InstallRequirement] = []
diff --git a/pip_audit/_dependency_source/resolvelib/pypi_provider.py b/pip_audit/_dependency_source/resolvelib/pypi_provider.py
index 683d861a..f5bc2639 100644
--- a/pip_audit/_dependency_source/resolvelib/pypi_provider.py
+++ b/pip_audit/_dependency_source/resolvelib/pypi_provider.py
@@ -26,14 +26,18 @@
 import html5lib
 import requests
 from cachecontrol import CacheControl
-from packaging.requirements import Requirement
+from packaging.requirements import InvalidRequirement, Requirement
 from packaging.specifiers import InvalidSpecifier, SpecifierSet
 from packaging.utils import canonicalize_name, parse_sdist_filename, parse_wheel_filename
 from packaging.version import Version
 from resolvelib.providers import AbstractProvider
 from resolvelib.resolvers import RequirementInformation
 
-from pip_audit._dependency_source import RequirementHashes, UnsupportedHashAlgorithm
+from pip_audit._dependency_source import (
+    InvalidRequirementSpecifier,
+    RequirementHashes,
+    UnsupportedHashAlgorithm,
+)
 from pip_audit._service import SkippedDependency
 from pip_audit._state import AuditState
 from pip_audit._util import python_version
@@ -134,7 +138,16 @@ def _get_dependencies(self) -> Iterator[Requirement]:
         extras = self.extras if self.extras else [""]
 
         for d in deps:
-            r = Requirement(d)
+            # NOTE: packaging 22 and later are more strict about PEP 440 requirements,
+            # meaning that pre-existing packages might have invalid requirements
+            # specifiers in their dependency sets (e.g. `pytz (>dev)`).
+            try:
+                r = Requirement(d)
+            except InvalidRequirement as exc:
+                raise InvalidRequirementSpecifier(
+                    f"{self.name} has invalid requirement '{d}': {exc}"
+                )
+
             if r.marker is None:
                 yield r
             else:
@@ -440,49 +453,51 @@ def find_matches(
         for r in requirements:
             extras |= r.extras
 
-        # Need to pass the extras to the search, so they
-        # are added to the candidate at creation - we
-        # treat candidates as immutable once created.
-        all_candidates = get_project_from_indexes(
-            self.index_urls,
-            self.session,
-            identifier,
-            requirements,
-            extras,
-            self.req_hashes,
-            self.timeout,
-            self._state,
-        )
-
-        candidates: list[ResolvedCandidate]
         try:
-            candidates = sorted(
-                [
-                    candidate
-                    for candidate in all_candidates
-                    if candidate.version not in bad_versions
-                    # NOTE(ww): We use `filter(...)` instead of checking
-                    # `candidate.version in r.specifier` because the former has subtle (and PEP 440
-                    # mandated) behavior around prereleases. Specifically, `filter(...)`
-                    # returns prereleases even if not explicitly configured, but only if
-                    # there are no non-prereleases.
-                    # See: https://github.com/pypa/pip-audit/issues/472
-                    and all([any(r.specifier.filter((candidate.version,))) for r in requirements])
-                    # HACK(ww): Additionally check that each candidate's name matches the
-                    # expected project name (identifier).
-                    # This technically shouldn't be required, but parsing distribution names
-                    # from package indices is imprecise/unreliable when distribution filenames
-                    # are PEP 440 compliant but not normalized.
-                    # See: https://github.com/pypa/packaging/issues/527
-                    and candidate.name == identifier
-                ],
-                key=attrgetter("version", "is_wheel"),
-                reverse=True,
+            # Need to pass the extras to the search, so that  they are added to the candidate at
+            # creation, since we treat candidates as immutable once created.
+            # We also eagerly collect the candidate list here, to pull any "not found"
+            # exceptions out before doing candidate filtering below.
+            all_candidates = list(
+                get_project_from_indexes(
+                    self.index_urls,
+                    self.session,
+                    identifier,
+                    requirements,
+                    extras,
+                    self.req_hashes,
+                    self.timeout,
+                    self._state,
+                )
             )
-        except PyPINotFoundError as e:
-            yield SkippedCandidate(name=identifier, skip_reason=str(e))
+        except PyPINotFoundError as exc:
+            yield SkippedCandidate(name=identifier, skip_reason=str(exc))
             return
 
+        candidates: list[ResolvedCandidate] = sorted(
+            [
+                candidate
+                for candidate in all_candidates
+                if candidate.version not in bad_versions
+                # NOTE(ww): We use `filter(...)` instead of checking
+                # `candidate.version in r.specifier` because the former has subtle (and PEP 440
+                # mandated) behavior around prereleases. Specifically, `filter(...)`
+                # returns prereleases even if not explicitly configured, but only if
+                # there are no non-prereleases.
+                # See: https://github.com/pypa/pip-audit/issues/472
+                and all([any(r.specifier.filter((candidate.version,))) for r in requirements])
+                # HACK(ww): Additionally check that each candidate's name matches the
+                # expected project name (identifier).
+                # This technically shouldn't be required, but parsing distribution names
+                # from package indices is imprecise/unreliable when distribution filenames
+                # are PEP 440 compliant but not normalized.
+                # See: https://github.com/pypa/packaging/issues/527
+                and candidate.name == identifier
+            ],
+            key=attrgetter("version", "is_wheel"),
+            reverse=True,
+        )
+
         logger.debug(f"{identifier} has candidates: {candidates}")
 
         # If we have multiple candidates for a single version and some are wheels,
diff --git a/test/dependency_source/resolvelib/test_pypi_provider.py b/test/dependency_source/resolvelib/test_pypi_provider.py
index 171e7e9a..608de45e 100644
--- a/test/dependency_source/resolvelib/test_pypi_provider.py
+++ b/test/dependency_source/resolvelib/test_pypi_provider.py
@@ -1,3 +1,4 @@
+from email.message import Message
 from pathlib import Path
 from subprocess import CalledProcessError
 
@@ -6,12 +7,13 @@
 from packaging.version import Version
 
 from pip_audit._dependency_source import RequirementHashes
+from pip_audit._dependency_source.interface import InvalidRequirementSpecifier
 from pip_audit._dependency_source.resolvelib import pypi_provider
 from pip_audit._dependency_source.resolvelib.pypi_provider import ResolvedCandidate
 from pip_audit._virtual_env import VirtualEnvError
 
 
-class TestCandidate:
+class TestResolvedCandidate:
     def test_get_metadata_for_sdist_venv_create_fails(self, monkeypatch):
         virtualenv_obj = pretend.stub(
             create=pretend.call_recorder(
@@ -53,6 +55,30 @@ def test_get_metadata_for_sdist_venv_create_fails(self, monkeypatch):
             "Installing source distribution in isolated environment for fakepkg (1.0.0)"
         )
 
+    @pytest.mark.parametrize("invalid", ["pytz (>dev)", "fakedep>=3.*"])
+    def test_get_dependencies_invalid_req_specifer(self, invalid, monkeypatch):
+        candidate = ResolvedCandidate(
+            "fakepkg",
+            "fakepkg",
+            Path("fakepath"),
+            Version("1.0.0"),
+            url="hxxps://fake.url",
+            extras=set(),
+            is_wheel=False,
+            reqs=[],
+            session=pretend.stub(),
+            timeout=None,
+            state=pretend.stub(),
+            req_hashes=RequirementHashes(),
+        )
+
+        metadata = Message()
+        metadata["Requires-Dist"] = invalid
+        monkeypatch.setattr(candidate, "_metadata", metadata)
+
+        with pytest.raises(InvalidRequirementSpecifier):
+            list(candidate._get_dependencies())
+
 
 def test_get_project_from_index_relative_url():
     data = """