This book reviews the history of the interface between morpho-syntax and phonology roughly since World War II. Structuralist and generative interface thinking is presented chronologically, but also theory by theory from the point of view of a historically interested observer who however in the last third of the book distills lessons in order to assess present-day interface theories, and to establish a catalogue of properties that a correct interface theory should or must not have. The book also introduces modularity, the rationalist theory of the (human) cognitive system that underlies the generative approach to language, from a Cognitive Science perspective. Modularity is used as a referee for interface theories in the book. Finally, the book locates the interface debate in the landscape of current minimalist syntax and phase theory and fosters intermodular argumentation: how can we use properties of morpho-syntactic theory in order to argue for or against competing theories of phonology (and vice-versa)?