The diversity of languages contrasts with the universality of much of the communicational infrastructure that makes language possible. An important component of this infrastructure is the turn-taking system of conversation, the Stephen Levinsoncore ecological niche for language use. This system puts intense pressure on language processing: cross-linguistically, we mostly respond within 200 milliseconds, even though language encoding takes at least three times as long. It can be shown using many different measures (e.g. response times, breathing, EEG) that we beat the clock by predicting what the other is going to say and starting production as soon as we can. This raises interesting questions about why this system is the way it is, what functional pressures it puts on language structure and language diversity, and how it originated, which I will briefly address. I will argue that the current system can best be understood within an evolutionary context in which the turn-taking system was antecedent to the complexities of modern language so that increasingly complex messages became squeezed into short turns, with the consequence of extreme compression, inference enrichment of the Gricean kind, a tendency for fixed word orders, amongst other things. Some support for this account can be found in ontogenetic and phylogenetic studies of turn-taking which I will briefly review.