How do we communicate meaningfully? While meaning is at the core of many theories of language, it has proven notoriously difficult to formalize. The traditional approach has been to assume that words convey a certain determinate content, which can participate in hierarchical syntactic structures. Language, on this view, is just a vehicle for encoding our thoughts and decoding those of others, or of 'packing' and 'unpacking' content into linguistic form. If this is right, it should be possible to specify a one-to-one mapping between the form and meaning of any given utterance, such that we can "say what we mean". Unfortunately, and despite the intuitive appeal of this approach, compositionality has run aground against a number of serious empirical and epistemological challenges. Where does this leave us? In this talk, I will sketch an alternative perspective of language as a predictive, collaborative enterprise, a perspective which is grounded in empirical studies on the importance of time in word learning, and corpus investigations into how languages use word order to manage a trade-off between efficiency and learnability. My interest will be to elaborate how principles from learning and information theory can constrain and reshape our understanding of what communication is, and the place of meaning in it.