diff --git a/CHANGES.rst b/CHANGES.rst
index 3482d02..95c553f 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -1,3 +1,13 @@
+v3.11.0
+=======
+
+* #85: Added support for new methods on ``Path``:
+
+  - ``match``
+  - ``glob`` and ``rglob``
+  - ``relative_to``
+  - ``is_symlink``
+
 v3.10.0
 =======
 
diff --git a/tests/test_zipp.py b/tests/test_zipp.py
index cac2cde..1e17870 100644
--- a/tests/test_zipp.py
+++ b/tests/test_zipp.py
@@ -403,6 +403,52 @@ def test_root_unnamed(self, alpharep):
         assert sub.name == "b"
         assert sub.parent
 
+    @pass_alpharep
+    def test_match_and_glob(self, alpharep):
+        root = zipp.Path(alpharep)
+        assert not root.match("*.txt")
+
+        assert list(root.glob("b/c.*")) == [zipp.Path(alpharep, "b/c.txt")]
+
+        files = root.glob("**/*.txt")
+        assert all(each.match("*.txt") for each in files)
+
+        assert list(root.glob("**/*.txt")) == list(root.rglob("*.txt"))
+
+    def test_glob_empty(self):
+        root = zipp.Path(zipfile.ZipFile(io.BytesIO(), 'w'))
+        with self.assertRaises(ValueError):
+            root.glob('')
+
+    @pass_alpharep
+    def test_eq_hash(self, alpharep):
+        root = zipp.Path(alpharep)
+        assert root == zipp.Path(alpharep)
+
+        assert root != (root / "a.txt")
+        assert (root / "a.txt") == (root / "a.txt")
+
+        root = zipp.Path(alpharep)
+        assert root in {root}
+
+    @pass_alpharep
+    def test_is_symlink(self, alpharep):
+        """
+        See python/cpython#82102 for symlink support beyond this object.
+        """
+
+        root = zipp.Path(alpharep)
+        assert not root.is_symlink()
+
+    @pass_alpharep
+    def test_relative_to(self, alpharep):
+        root = zipp.Path(alpharep)
+        relative = root.joinpath("b", "c.txt").relative_to(root / "b")
+        assert str(relative) == "c.txt"
+
+        relative = root.joinpath("b", "d", "e.txt").relative_to(root / "b")
+        assert str(relative) == "d/e.txt"
+
     @pass_alpharep
     def test_inheritance(self, alpharep):
         cls = type('PathChild', (zipp.Path,), {})
diff --git a/zipp/__init__.py b/zipp/__init__.py
index c1f3632..ad01e27 100644
--- a/zipp/__init__.py
+++ b/zipp/__init__.py
@@ -4,6 +4,8 @@
 import itertools
 import contextlib
 import pathlib
+import re
+import fnmatch
 
 from .py310compat import text_encoding
 
@@ -243,6 +245,18 @@ def __init__(self, root, at=""):
         self.root = FastLookup.make(root)
         self.at = at
 
+    def __eq__(self, other):
+        """
+        >>> Path(zipfile.ZipFile(io.BytesIO(), 'w')) == 'foo'
+        False
+        """
+        if self.__class__ is not other.__class__:
+            return NotImplemented
+        return (self.root, self.at) == (other.root, other.at)
+
+    def __hash__(self):
+        return hash((self.root, self.at))
+
     def open(self, mode='r', *args, pwd=None, **kwargs):
         """
         Open this entry as text or binary following the semantics
@@ -313,6 +327,38 @@ def iterdir(self):
         subs = map(self._next, self.root.namelist())
         return filter(self._is_child, subs)
 
+    def match(self, path_pattern):
+        return pathlib.Path(self.at).match(path_pattern)
+
+    def is_symlink(self):
+        """
+        Return whether this path is a symlink. Always false (python/cpython#82102).
+        """
+        return False
+
+    def _descendants(self):
+        for child in self.iterdir():
+            yield child
+            if child.is_dir():
+                yield from child._descendants()
+
+    def glob(self, pattern):
+        if not pattern:
+            raise ValueError("Unacceptable pattern: {!r}".format(pattern))
+
+        matches = re.compile(fnmatch.translate(pattern)).fullmatch
+        return (
+            child
+            for child in self._descendants()
+            if matches(str(child.relative_to(self)))
+        )
+
+    def rglob(self, pattern):
+        return self.glob(f'**/{pattern}')
+
+    def relative_to(self, other, *extra):
+        return posixpath.relpath(str(self), str(other.joinpath(*extra)))
+
     def __str__(self):
         return posixpath.join(self.root.filename, self.at)