Distributional semantics provides multi-dimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown in a large body of work in computational linguistics; yet, its impact in theoretical linguistics has so far been limited. This survey provides a critical discussion of the literature on distributional semantics, with an emphasis on methods and results that are of relevance for theoretical linguistics, in three areas: semantic change, polysemy, and the grammar-semantics interface.