This book explores theoretical issues of the syntax-phonology interface within the Minimalist Program of linguistic theory and proposes an entirely new approach to prosodic categories. Conceptual as well as empirical questions are addressed, concerning how syntactic objects are mapped to the sensorimotor system through the processes of externalization. Elaborating on recent progress in the theories of labelling and workspace-based syntactic derivation, this book further develops a null theory of the prosodic domains, and recasts these as the domains of interpretation that are reducible to more fundamental concepts of linguistic theory. Phonological phrases are characterized by Minimal Search, a third factor principle of efficient computation. Intonational phrases are taken to be reflexes of the termination of syntactic derivation, which is formulated in terms of the workspace to which MERGE applies. This book explores the new implications this theory has for the general architecture of grammar as well as for linguistic interfaces. It provides a comprehensive review of the development of theories of the syntax-phonology interface from over the past three decades. The book is well-suited for general linguistic readers as well as phonologists, syntacticians, and any linguist interested in interface research.