diff --git a/flit/upload.py b/flit/upload.py
index afd5f798..4a9697c8 100644
--- a/flit/upload.py
+++ b/flit/upload.py
@@ -226,7 +226,7 @@ def build_post_data(action, metadata:Metadata):
         "version": metadata.version,
 
         # additional meta-data
-        "metadata_version": '2.1',
+        "metadata_version": '2.3',
         "summary": metadata.summary,
         "home_page": metadata.home_page,
         "author": metadata.author,
diff --git a/flit_core/flit_core/common.py b/flit_core/flit_core/common.py
index 9f2b9204..6625224b 100644
--- a/flit_core/flit_core/common.py
+++ b/flit_core/flit_core/common.py
@@ -347,8 +347,9 @@ class Metadata(object):
     obsoletes_dist = ()
     requires_external = ()
     provides_extra = ()
+    dynamic = ()
 
-    metadata_version = "2.1"
+    metadata_version = "2.3"
 
     def __init__(self, data):
         data = data.copy()
@@ -359,9 +360,31 @@ def __init__(self, data):
             assert hasattr(self, k), "data does not have attribute '{}'".format(k)
             setattr(self, k, v)
 
-    def _normalise_name(self, n):
+    def _normalise_field_name(self, n):
         return n.lower().replace('-', '_')
 
+    def _normalise_core_metadata_name(self, name):
+        # Normalized Names (PEP 503)
+        return re.sub(r"[-_.]+", "-", name).lower()
+
+    def _extract_extras(self, req):
+        match = re.search(r'\[([^]]*)\]', req)
+        if match:
+            list_str = match.group(1)
+            return [item.strip() for item in list_str.split(',')]
+        else:
+            return None
+    
+    def _normalise_requires_dist(self, req):
+        extras = self._extract_extras(req)
+        if extras:
+            normalised_extras = [self._normalise_core_metadata_name(extra) for extra in extras]
+            normalised_extras_str = ', '.join(normalised_extras)
+            normalised_req = re.sub(r'\[([^]]*)\]', f"[{normalised_extras_str}]", req)
+            return normalised_req
+        else:
+            return req
+
     def write_metadata_file(self, fp):
         """Write out metadata in the email headers format"""
         fields = [
@@ -383,11 +406,11 @@ def write_metadata_file(self, fp):
         ]
 
         for field in fields:
-            value = getattr(self, self._normalise_name(field))
+            value = getattr(self, self._normalise_field_name(field))
             fp.write(u"{}: {}\n".format(field, value))
 
         for field in optional_fields:
-            value = getattr(self, self._normalise_name(field))
+            value = getattr(self, self._normalise_field_name(field))
             if value is not None:
                 # TODO: verify which fields can be multiline
                 # The spec has multiline examples for Author, Maintainer &
@@ -400,13 +423,15 @@ def write_metadata_file(self, fp):
             fp.write(u'Classifier: {}\n'.format(clsfr))
 
         for req in self.requires_dist:
-            fp.write(u'Requires-Dist: {}\n'.format(req))
+            normalised_req = self._normalise_requires_dist(req)
+            fp.write(u'Requires-Dist: {}\n'.format(normalised_req))
 
         for url in self.project_urls:
             fp.write(u'Project-URL: {}\n'.format(url))
 
         for extra in self.provides_extra:
-            fp.write(u'Provides-Extra: {}\n'.format(extra))
+            normalised_extra = self._normalise_core_metadata_name(extra)
+            fp.write(u'Provides-Extra: {}\n'.format(normalised_extra))
 
         if self.description is not None:
             fp.write(u'\n' + self.description + u'\n')
diff --git a/flit_core/flit_core/tests/test_common.py b/flit_core/flit_core/tests/test_common.py
index b6d62905..824fa5de 100644
--- a/flit_core/flit_core/tests/test_common.py
+++ b/flit_core/flit_core/tests/test_common.py
@@ -156,3 +156,52 @@ def test_metadata_multiline(tmp_path):
     assert msg['Version'] == d['version']
     assert [l.lstrip() for l in msg['Author'].splitlines()] == d['author'].splitlines()
     assert not msg.defects
+
+@pytest.mark.parametrize(
+    ("requires_dist", "expected_result"),
+    [
+        ('foo [extra_1, extra.2, extra-3, extra__4, extra..5, extra--6]', 'foo [extra-1, extra-2, extra-3, extra-4, extra-5, extra-6]'),
+        ('foo', 'foo'),
+        ('foo[bar]', 'foo[bar]'),
+        # https://packaging.python.org/en/latest/specifications/core-metadata/#requires-dist-multiple-use
+        ('pkginfo', 'pkginfo'),
+        ('zope.interface (>3.5.0)', 'zope.interface (>3.5.0)'),
+        ("pywin32 >1.0; sys_platform == 'win32'", "pywin32 >1.0; sys_platform == 'win32'"),
+    ],
+)
+def test_metadata_2_3_requires_dist(requires_dist, expected_result):
+    d = {
+        'name': 'foo',
+        'version': '1.0',
+        'requires_dist': [requires_dist],
+    }
+    md = Metadata(d)
+    sio = StringIO()
+    md.write_metadata_file(sio)
+    sio.seek(0)
+
+    msg = email.parser.Parser(policy=email.policy.compat32).parse(sio)
+    assert msg['Requires-Dist'] == expected_result
+    assert not msg.defects
+
+@pytest.mark.parametrize(
+    ("provides_extra", "expected_result"),
+    [
+        ('foo', 'foo'),
+        ('foo__bar..baz', 'foo-bar-baz'),
+    ],
+)
+def test_metadata_2_3_provides_extra(provides_extra, expected_result):
+    d = {
+        'name': 'foo',
+        'version': '1.0',
+        'provides_extra': [provides_extra],
+    }
+    md = Metadata(d)
+    sio = StringIO()
+    md.write_metadata_file(sio)
+    sio.seek(0)
+
+    msg = email.parser.Parser(policy=email.policy.compat32).parse(sio)
+    assert msg['Provides-Extra'] == expected_result
+    assert not msg.defects