diff --git a/pymbolic/mapper/subst_applier.py b/pymbolic/mapper/subst_applier.py
new file mode 100644
index 00000000..2b030399
--- /dev/null
+++ b/pymbolic/mapper/subst_applier.py
@@ -0,0 +1,45 @@
+from __future__ import annotations
+
+
+__copyright__ = "Copyright (C) 2021 Thomas Gibson"
+
+__license__ = """
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+"""
+
+from pymbolic.mapper import IdentityMapper
+
+
+class SubstitutionApplier(IdentityMapper):
+    """todo.
+    """
+
+    def map_substitution(self, expr, current_substs):
+        new_substs = current_substs.copy()
+        new_substs.update(
+            {variable: self.rec(value, current_substs)
+            for variable, value in zip(expr.variables, expr.values)})
+        return self.rec(expr.child, new_substs)
+
+    def map_variable(self, expr, current_substs):
+        return current_substs.get(expr.name, expr)
+
+    def __call__(self, expr):
+        current_substs = {}
+        return super().__call__(expr, current_substs)
diff --git a/pymbolic/primitives.py b/pymbolic/primitives.py
index 838bad1a..496a0427 100644
--- a/pymbolic/primitives.py
+++ b/pymbolic/primitives.py
@@ -1551,7 +1551,24 @@ def get_extra_properties(self):
 
 @expr_dataclass()
 class Substitution(Expression):
-    """Work-alike of sympy's Subs."""
+    """A (deferred) substitution applicable to a subexpression.
+
+    See also sympy's ``Subs``.
+
+    .. attribute:: child
+
+        The sub-:class:`Expression` to which the substitution is to be applied.
+
+    .. attribute:: variables
+
+        A sequence of string identifiers of the variables to be replaced with
+        their corresponding entry in :attr:`values`.
+
+    .. attribute:: values
+
+        A sequence of sub-:class:`Expression` objects corresponding to each
+        string identifier in :attr:`variables`.
+    """
 
     child: ExpressionT
     variables: tuple[str, ...]
diff --git a/test/test_pymbolic.py b/test/test_pymbolic.py
index eb8ac768..b49333e2 100644
--- a/test/test_pymbolic.py
+++ b/test/test_pymbolic.py
@@ -1016,6 +1016,40 @@ def test_nodecount():
     assert get_num_nodes(expr) == 12
 
 
+def test_subst_applier():
+    x = prim.Variable("x")
+    y = prim.Variable("y")
+    z = prim.Variable("z")
+
+    from pymbolic.mapper.substitutor import substitute as subst_actual
+
+    def subst_deferred(expr, **kwargs):
+        variables = []
+        values = []
+        for name, value in kwargs.items():
+            variables.append(name)
+            values.append(value)
+        return prim.Substitution(expr, variables, values)
+
+    from pymbolic.mapper.subst_applier import SubstitutionApplier
+    sapp = SubstitutionApplier()
+
+    results = []
+    for subst in [subst_actual, subst_deferred]:
+        expr = subst(x + y, x=5*y)
+        print(expr)
+        expr = subst(subst(expr**2, y=z) - subst(expr, y=x), x=y)
+        print(expr)
+        expr = sapp(expr)
+        print(expr)
+
+        results.append(sapp(expr))
+        print("--------")
+
+    result_actual, result_deferred = results
+    assert result_actual == result_deferred
+
+
 def test_python_ast_interop_roundtrip():
     from pymbolic.interop.ast import ASTToPymbolic, PymbolicToASTMapper