diff --git a/news/5892.bugfix b/news/5892.bugfix
new file mode 100644
index 00000000000..4f25ee08e9b
--- /dev/null
+++ b/news/5892.bugfix
@@ -0,0 +1 @@
+Improve handling of file URIs: correctly handle `file://localhost/...` and don't try to use UNC paths on Unix.
diff --git a/src/pip/_internal/download.py b/src/pip/_internal/download.py
index 2bbe1762cda..22eaa6b246c 100644
--- a/src/pip/_internal/download.py
+++ b/src/pip/_internal/download.py
@@ -473,9 +473,17 @@ def url_to_path(url):
 
     _, netloc, path, _, _ = urllib_parse.urlsplit(url)
 
-    # if we have a UNC path, prepend UNC share notation
-    if netloc:
+    if not netloc or netloc == 'localhost':
+        # According to RFC 8089, same as empty authority.
+        netloc = ''
+    elif sys.platform == 'win32':
+        # If we have a UNC path, prepend UNC share notation.
         netloc = '\\\\' + netloc
+    else:
+        raise ValueError(
+            'non-local file URIs are not supported on this platform: %r'
+            % url
+        )
 
     path = urllib_request.url2pathname(netloc + path)
     return path
diff --git a/tests/unit/test_download.py b/tests/unit/test_download.py
index 532eb3fc3eb..2391f426022 100644
--- a/tests/unit/test_download.py
+++ b/tests/unit/test_download.py
@@ -1,5 +1,6 @@
 import hashlib
 import os
+import sys
 from io import BytesIO
 from shutil import copy, rmtree
 from tempfile import mkdtemp
@@ -125,11 +126,6 @@ def test_path_to_url_unix():
     assert path_to_url('file') == 'file://' + urllib_request.pathname2url(path)
 
 
-@pytest.mark.skipif("sys.platform == 'win32'")
-def test_url_to_path_unix():
-    assert url_to_path('file:///tmp/file') == '/tmp/file'
-
-
 @pytest.mark.skipif("sys.platform != 'win32'")
 def test_path_to_url_win():
     assert path_to_url('c:/tmp/file') == 'file:///C:/tmp/file'
@@ -139,10 +135,27 @@ def test_path_to_url_win():
     assert path_to_url('file') == 'file:' + urllib_request.pathname2url(path)
 
 
-@pytest.mark.skipif("sys.platform != 'win32'")
-def test_url_to_path_win():
-    assert url_to_path('file:///c:/tmp/file') == 'C:\\tmp\\file'
-    assert url_to_path('file://unc/as/path') == r'\\unc\as\path'
+@pytest.mark.parametrize("url,win_expected,non_win_expected", [
+    ('file:tmp', 'tmp', 'tmp'),
+    ('file:c:/path/to/file', r'C:\path\to\file', 'c:/path/to/file'),
+    ('file:/path/to/file', r'\path\to\file', '/path/to/file'),
+    ('file://localhost/tmp/file', r'\tmp\file', '/tmp/file'),
+    ('file://localhost/c:/tmp/file', r'C:\tmp\file', '/c:/tmp/file'),
+    ('file://somehost/tmp/file', r'\\somehost\tmp\file', None),
+    ('file:///tmp/file', r'\tmp\file', '/tmp/file'),
+    ('file:///c:/tmp/file', r'C:\tmp\file', '/c:/tmp/file'),
+])
+def test_url_to_path(url, win_expected, non_win_expected):
+    if sys.platform == 'win32':
+        expected_path = win_expected
+    else:
+        expected_path = non_win_expected
+
+    if expected_path is None:
+        with pytest.raises(ValueError):
+            url_to_path(url)
+    else:
+        assert url_to_path(url) == expected_path
 
 
 @pytest.mark.skipif("sys.platform != 'win32'")