We analyze the matching problem for bigraphs. In particular, we present an axiomatization of the static theory of binding bigraphs, a non-trivial extension of the axiomatization of pure bigraphs developed by Milner. Based directly on the term language resulting from the axiomatization we present a sound and complete inductive characterization of matching of binding bigraphs. Our results pave the way for an actual matching algorithm, as needed for an implementation of bigraphical reactive systems.