diff --git a/discord/permissions.py b/discord/permissions.py
index 8d0dbe02a..bc74536c3 100644
--- a/discord/permissions.py
+++ b/discord/permissions.py
@@ -36,6 +36,18 @@ class Permissions:
     +-----------+------------------------------------------+
     | x != y    | Checks if two permissions are not equal. |
     +-----------+------------------------------------------+
+    | x <= y    | Checks if a permission is a subset       |
+    |           | of another permission.                   |
+    +-----------+------------------------------------------+
+    | x >= y    | Checks if a permission is a superset     |
+    |           | of another permission.                   |
+    +-----------+------------------------------------------+
+    | x < y     | Checks if a permission is a strict       |
+    |           | subset of another permission.            |
+    +-----------+------------------------------------------+
+    | x > y     | Checks if a permission is a strict       |
+    |           | superset of another permission.          |
+    +-----------+------------------------------------------+
     | hash(x)   | Return the permission's hash.            |
     +-----------+------------------------------------------+
 
@@ -63,6 +75,33 @@ class Permissions:
     def __hash__(self):
         return hash(self.value)
 
+    def is_subset(self, other):
+        """Returns True if other has the same or fewer permissions as self."""
+        if isinstance(other, Permissions):
+            return (self.value & other.value) == self.value
+        else:
+            raise TypeError("cannot compare {} with {}".format(self.__class__.__name__, other.__class__name))
+
+    def is_superset(self, other):
+        """Returns True if other has the same or more permissions as self."""
+        if isinstance(other, Permissions):
+            return (self.value | other.value) == self.value
+        else:
+            raise TypeError("cannot compare {} with {}".format(self.__class__.__name__, other.__class__name))
+
+    def is_strict_subset(self, other):
+        """Returns True if the permissions on other are a strict subset of those on self."""
+        return self.is_subset(other) and self != other
+
+    def is_strict_superset(self, other):
+        """Returns True if the permissions on other are a strict superset of those on self."""
+        return self.is_superset(other) and self != other
+
+    __le__ = is_subset
+    __ge__ = is_superset
+    __lt__ = is_strict_subset
+    __gt__ = is_strict_superset
+
     @classmethod
     def none(cls):
         """A factory method that creates a :class:`Permissions` with all