This book addresses the fundamental issues in the phase-based approach to the mental computation of language that have arisen from the recent developments in the Minimalist Program. Leading linguists and promising young scholars from all over the world focus on two topics that are in the centre of current theorizing in syntax - the interaction of syntax with the conceptual-intentional and sensorimotor interfaces, and current formulations of phase theory. Phases are a recent way of theorizing and modelling the computational system of human language in relation to the interfaces between syntactic derivation and logical form and phonological form. What exactly, for example, does Spell-Out do? Where do morphology and phonology kick in? Are these two levels of representation sufficient, too many, or not enough? How can the interaction between syntax and prosody be formally represented? The authors discuss these and other central questions including the degree to which phases are the right way to think about the dynamic system of language. They consider how far the answers are likely to come from conceptual and theoretical considerations or from experimental and empirical research, which key components might be missing, and how the system can be improved. Both in its parts and as a whole, the book explains and contributes to some of the liveliest and most central debates in contemporary linguistics.