In this paper we present a theory of binding structures, and give examples of its application to rewriting. We define the set of binding structures as an abstract algebra, and define a general notion of parameterized homomorphism. A variety of operations on binding structures are presented as homomorphisms, and a collection of properties useful for developing applications is given. Three applications are presented: a generalized notion of term rewriting: a theory of unification for binding structures; and a set of structures and primitive rules intended to serve as a basis for design of rewriting components for (quantified) first-order reasoning systems.
