In this position paper we argue that an adequate semantic model must account for language in use, taking into account how discourse context affects the meaning of words and larger linguistic units. Distributional semantic models are very attractive models of meaning mainly because they capture conceptual aspects and are automatically induced from natural language data. However, they need to be extended in order to account for language use in a discourse or dialogue context. We discuss phenomena that the new generation of distributional semantic models should capture, and propose concrete tasks on which they could be tested.