This paper introduces Match Theory, an Optimality-Theoretic approach to the syntax-phonology interface proposed by Selkirk (2011). The theory states that a family of Match constraints favor syntax-prosody isomorphism, but that these can be outranked by constraints on prosodic wellformedness and/or information structure, resulting in certain principled mismatches. We compare Match Theory to previous OT approaches involving edge-alignment, and discuss several outstanding issues for Match Theory such as the proper treatment of asymmetries in syntax-prosody matching.