Distributional semantics provides multidimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown by a large body of research in computational linguistics; yet, its impact in theoretical linguistics has so far been limited. This review provides a critical discussion of the literature on distributional semantics, with an emphasis on methods and results that are relevant for theoretical linguistics, in three areas: semantic change, polysemy and composition, and the grammar-semantics interface (specifically, the interface of semantics with syntax and with derivational morphology). The goal of this review is to foster greater cross-fertilization of theoretical and computational approaches to language as a means to advance our collective knowledge of how it works.