diff --git a/Lib/xml/etree/ElementPath.py b/Lib/xml/etree/ElementPath.py
index b670d58..cfe72f2 100644
--- a/Lib/xml/etree/ElementPath.py
+++ b/Lib/xml/etree/ElementPath.py
@@ -99,13 +99,70 @@
                 parent_map[e] = p
     return parent_map
 
+
+
+def _is_wildcard_tag(tag):
+    return tag[:3] == '{*}' or tag[-2:] == '}*'
+
+
+def _prepare_tag(tag):
+    _isinstance, _str = isinstance, str
+    if tag == '{*}*':
+        # Same as '*', but no comments or processing instructions.
+        # It can be a surprise that '*' includes those, but there is no
+        # justification for '{*}*' doing the same.
+        def select(context, result):
+            for elem in result:
+                if _isinstance(elem.tag, _str):
+                    yield elem
+    elif tag == '{}*':
+        # Any tag that is not in a namespace.
+        def select(context, result):
+            for elem in result:
+                el_tag = elem.tag
+                if _isinstance(el_tag, _str) and el_tag[0] != '{':
+                    yield elem
+    elif tag[:3] == '{*}':
+        # The tag in any (or no) namespace.
+        suffix = tag[2:]  # '}name'
+        no_ns = slice(-len(suffix), None)
+        tag = tag[3:]
+        def select(context, result):
+            for elem in result:
+                el_tag = elem.tag
+                if el_tag == tag or _isinstance(el_tag, _str) and el_tag[no_ns] == suffix:
+                    yield elem
+    elif tag[-2:] == '}*':
+        # Any tag in the given namespace.
+        ns = tag[:-1]
+        ns_only = slice(None, len(ns))
+        def select(context, result):
+            for elem in result:
+                el_tag = elem.tag
+                if _isinstance(el_tag, _str) and el_tag[ns_only] == ns:
+                    yield elem
+    else:
+        raise RuntimeError(f"internal parser error, got {tag}")
+    return select
+
+
 def prepare_child(next, token):
     tag = token[1]
-    def select(context, result):
-        for elem in result:
-            for e in elem:
-                if e.tag == tag:
-                    yield e
+    if _is_wildcard_tag(tag):
+        select_tag = _prepare_tag(tag)
+        def select(context, result):
+            def select_child(result):
+                for elem in result:
+                    yield from elem
+            return select_tag(context, select_child(result))
+    else:
+        if tag[:2] == '{}':
+            tag = tag[2:]  # '{}tag' == 'tag'
+        def select(context, result):
+            for elem in result:
+                for e in elem:
+                    if e.tag == tag:
+                        yield e
     return select
 
 def prepare_star(next, token):
@@ -130,11 +187,24 @@
         tag = token[1]
     else:
         raise SyntaxError("invalid descendant")
-    def select(context, result):
-        for elem in result:
-            for e in elem.iter(tag):
-                if e is not elem:
-                    yield e
+
+    if _is_wildcard_tag(tag):
+        select_tag = _prepare_tag(tag)
+        def select(context, result):
+            def select_child(result):
+                for elem in result:
+                    for e in elem.iter():
+                        if e is not elem:
+                            yield e
+            return select_tag(context, select_child(result))
+    else:
+        if tag[:2] == '{}':
+            tag = tag[2:]  # '{}tag' == 'tag'
+        def select(context, result):
+            for elem in result:
+                for e in elem.iter(tag):
+                    if e is not elem:
+                        yield e
     return select
 
 def prepare_parent(next, token):