diff --git a/pytools/tag.py b/pytools/tag.py
index e9a4cc69f766d0379bdc01334f2f5d40c30c7cc0..b943d954fc48fcb03b0d78bd7d291d566c8d78ef 100644
--- a/pytools/tag.py
+++ b/pytools/tag.py
@@ -1,10 +1,12 @@
 from dataclasses import dataclass
-from typing import Tuple, Any, FrozenSet
+from typing import Tuple, Any, FrozenSet, Union, Iterable, TypeVar
+from pytools import memoize
 
 __copyright__ = """
-Copyright (C) 2020 Andreas Kloeckner
+Copyright (C) 2020 Andreas Klöckner
 Copyright (C) 2020 Matt Wala
 Copyright (C) 2020 Xiaoyu Wei
+Copyright (C) 2020 Nicholas Christensen
 """
 
 __license__ = """
@@ -27,6 +29,7 @@ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 """
 
+
 # {{{ docs
 
 __doc__ = """
@@ -34,6 +37,7 @@ __doc__ = """
 Tag Interface
 ---------------
 
+.. autoclass:: Taggable
 .. autoclass:: Tag
 .. autoclass:: UniqueTag
 
@@ -41,14 +45,14 @@ Supporting Functionality
 ------------------------
 
 .. autoclass:: DottedName
+.. autoclass:: NonUniqueTagError
 
 """
 
-# }}}
-
+#  }}}
 
-# {{{ dotted name
 
+#  {{{ dotted name
 
 class DottedName:
     """
@@ -89,6 +93,7 @@ class DottedName:
 
 # }}}
 
+
 # {{{ tag
 
 tag_dataclass = dataclass(init=True, eq=True, frozen=True, repr=True)
@@ -117,16 +122,138 @@ class Tag:
     def tag_name(self) -> DottedName:
         return DottedName.from_class(type(self))
 
+# }}}
+
+
+# {{{ unique tag
 
 class UniqueTag(Tag):
     """
-    Only one instance of this type of tag may be assigned
-    to a single tagged object.
+    A superclass for tags that are unique on each :class:`Taggable`.
+
+    Each instance of :class:`Taggable` may have no more than one
+    instance of each subclass of :class:`UniqueTag` in its
+    set of `tags`. Multiple `UniqueTag` instances of
+    different (immediate) subclasses are allowed.
     """
     pass
 
+# }}}
+
 
 TagsType = FrozenSet[Tag]
+TagOrIterableType = Union[Iterable[Tag], Tag, None]
+T_co = TypeVar("T_co", bound="Taggable")
+
+
+# {{{ taggable
+
+@memoize
+def _immediate_unique_tag_descendants(cls):
+    if UniqueTag in cls.__bases__:
+        return frozenset([cls])
+    else:
+        result = frozenset()
+        for base in cls.__bases__:
+            result = result | _immediate_unique_tag_descendants(base)
+        return result
+
+
+class NonUniqueTagError(ValueError):
+    """
+    Raised when a :class:`Taggable` object is instantiated with more
+    than one :class:`UniqueTag` instances of the same subclass in
+    its set of tags.
+    """
+    pass
+
+
+class Taggable:
+    """
+    Parent class for objects with a `tags` attribute.
+
+    .. attribute:: tags
+
+        A :class:`frozenset` of :class:`Tag` instances
+
+    .. method:: copy
+    .. method:: tagged
+    .. method:: without_tags
+
+    .. versionadded:: 2021.1
+    """
+
+    def __init__(self, tags: TagsType = frozenset()):
+        # For performance we assert rather than
+        # normalize the input.
+        assert isinstance(tags, FrozenSet)
+        assert all(isinstance(tag, Tag) for tag in tags)
+        self.tags = tags
+        self._check_uniqueness()
+
+    def _normalize_tags(self, tags: TagOrIterableType) -> TagsType:
+        if isinstance(tags, Tag):
+            t = frozenset([tags])
+        elif tags is None:
+            t = frozenset()
+        else:
+            t = frozenset(tags)
+        return t
+
+    def _check_uniqueness(self):
+        unique_tag_descendants = set()
+        for tag in self.tags:
+            tag_unique_tag_descendants = _immediate_unique_tag_descendants(
+                    type(tag))
+            intersection = unique_tag_descendants & tag_unique_tag_descendants
+            if intersection:
+                raise NonUniqueTagError("Multiple tags are direct subclasses of "
+                        "the following UniqueTag(s): "
+                        f"{', '.join(d.__name__ for d in intersection)}")
+            else:
+                unique_tag_descendants.update(tag_unique_tag_descendants)
+
+    def copy(self: T_co, **kwargs: Any) -> T_co:
+        """
+        Returns of copy of *self* with the specified tags. This method
+        should be overridden by subclasses.
+        """
+        raise NotImplementedError("The copy function is not implemented.")
+
+    def tagged(self: T_co, tags: TagOrIterableType) -> T_co:
+        """
+        Return a copy of *self* with the specified
+        tag or tags unioned. If *tags* is a :class:`pytools.tag.UniqueTag`
+        and other tags of this type are already present, an error is raised
+        Assumes `self.copy(tags=<NEW VALUE>)` is implemented.
+
+        :arg tags: An instance of :class:`Tag` or
+        an iterable with instances therein.
+        """
+        new_tags = self._normalize_tags(tags)
+        union_tags = self.tags | new_tags
+        cpy = self.copy(tags=union_tags)
+        return cpy
+
+    def without_tags(self: T_co,
+            tags: TagOrIterableType, verify_existence: bool = True) -> T_co:
+        """
+        Return a copy of *self* without the specified tags.
+        `self.copy(tags=<NEW VALUE>)` is implemented.
+
+        :arg tags: An instance of :class:`Tag` or an iterable with instances
+        therein.
+        :arg verify_existence: If set
+        to `True`, this method raises an exception if not all tags specified
+        for removal are present in the original set of tags. Default `True`
+        """
+
+        to_remove = self._normalize_tags(tags)
+        new_tags = self.tags - to_remove
+        if verify_existence and len(new_tags) > len(self.tags) - len(to_remove):
+            raise ValueError("A tag specified for removal was not present.")
+
+        return self.copy(tags=new_tags)
 
 # }}}
 
diff --git a/pytools/version.py b/pytools/version.py
index 99b6b21563e5660d93da0deb423168b95d50af55..e4c47bc9ed6a54934f00ad2e03256e2fa19c60f7 100644
--- a/pytools/version.py
+++ b/pytools/version.py
@@ -1,3 +1,3 @@
-VERSION = (2020, 4, 4)
+VERSION = (2021, 1)
 VERSION_STATUS = ""
 VERSION_TEXT = ".".join(str(x) for x in VERSION) + VERSION_STATUS
diff --git a/test/test_pytools.py b/test/test_pytools.py
index 0e8f99205afdeb98a76d53a2ddff52aaae3e4413..87b5d3a76d2d76e4a61e8343252e9b81cd7c767c 100644
--- a/test/test_pytools.py
+++ b/test/test_pytools.py
@@ -283,6 +283,93 @@ def test_make_obj_array_iteration():
 # }}}
 
 
+def test_tag():
+    from pytools.tag import Taggable, Tag, UniqueTag, NonUniqueTagError
+
+    # Need a subclass that defines the copy function in order to test.
+    class TaggableWithCopy(Taggable):
+
+        def copy(self, **kwargs):
+            return TaggableWithCopy(kwargs["tags"])
+
+    class FairRibbon(Tag):
+        pass
+
+    class BlueRibbon(FairRibbon):
+        pass
+
+    class RedRibbon(FairRibbon):
+        pass
+
+    class ShowRibbon(FairRibbon, UniqueTag):
+        pass
+
+    class BestInShowRibbon(ShowRibbon):
+        pass
+
+    class ReserveBestInShowRibbon(ShowRibbon):
+        pass
+
+    class BestInClassRibbon(FairRibbon, UniqueTag):
+        pass
+
+    best_in_show_ribbon = BestInShowRibbon()
+    reserve_best_in_show_ribbon = ReserveBestInShowRibbon()
+    blue_ribbon = BlueRibbon()
+    red_ribbon = RedRibbon()
+    best_in_class_ribbon = BestInClassRibbon()
+
+    # Test that instantiation fails if tags is not a FrozenSet of Tags
+    with pytest.raises(AssertionError):
+        TaggableWithCopy(tags=[best_in_show_ribbon, reserve_best_in_show_ribbon,
+                            blue_ribbon, red_ribbon])
+
+    # Test that instantiation fails if tags is not a FrozenSet of Tags
+    with pytest.raises(AssertionError):
+        TaggableWithCopy(tags=frozenset((1, reserve_best_in_show_ribbon, blue_ribbon,
+                                red_ribbon)))
+
+    # Test that instantiation fails if there are multiple instances
+    # of the same UniqueTag subclass
+    with pytest.raises(NonUniqueTagError):
+        TaggableWithCopy(tags=frozenset((best_in_show_ribbon,
+                            reserve_best_in_show_ribbon, blue_ribbon, red_ribbon)))
+
+    # Test that instantiation succeeds if there are multiple instances
+    # Tag subclasses.
+    t1 = TaggableWithCopy(frozenset([reserve_best_in_show_ribbon, blue_ribbon,
+                                    red_ribbon]))
+    assert t1.tags == frozenset((reserve_best_in_show_ribbon, red_ribbon,
+                                    blue_ribbon))
+
+    # Test that instantiation succeeds if there are multiple instances
+    # of UniqueTag of different subclasses.
+    t1 = TaggableWithCopy(frozenset([reserve_best_in_show_ribbon,
+                            best_in_class_ribbon, blue_ribbon,
+                                    blue_ribbon]))
+    assert t1.tags == frozenset((reserve_best_in_show_ribbon, best_in_class_ribbon,
+                                blue_ribbon))
+
+    # Test tagged() function
+    t2 = t1.tagged(red_ribbon)
+    print(t2.tags)
+    assert t2.tags == frozenset((reserve_best_in_show_ribbon, best_in_class_ribbon,
+                                blue_ribbon, red_ribbon))
+
+    # Test that tagged() fails if a UniqueTag of the same subclass
+    # is alredy present
+    with pytest.raises(NonUniqueTagError):
+        t1.tagged(best_in_show_ribbon)
+
+    # Test without_tags() function
+    t4 = t2.without_tags(red_ribbon)
+    assert t4.tags == t1.tags
+
+    # Test that without_tags() fails if the tag is not present.
+    with pytest.raises(ValueError):
+        t4.without_tags(red_ribbon)
+
+
 if __name__ == "__main__":
     if len(sys.argv) > 1:
         exec(sys.argv[1])