The path-breaking paper by Sacks, Schegloff & Jefferson (1974) on turn-taking was a crucial foundation stone in the establishment of CA: turn-taking gives conversation its essential character and its analysis can be exploited to shed light on 101 further topics. Despite continuing work by a handful of scholars, we have thus learnt to take the phenomenon largely for granted. But recent work now shows just how extraordinary the turn - taking phenomenon is from a cognitive perspective, and makes clear that there is still a great deal to be explained about how the system actually works in detail (e.g. how turn-ends are actually projected). In this paper,drawing on the joint work of our MPI Nijmegen research project, I will bring many different avenues of investigation – from human development, the phonetics of breathing and intonation, psycholog ical experimentation, brain -imaging and cross -cultural and cross -linguistic perspectives –to bear on the underlying issues about how the system works in real time. One central psycholinguistic puzzle is that speech encoding is very slow, but turn -transition very fast, implying much more extensive projection than had been commonly imagined. These different lines of investigation also hint at a phylogenetically ancient interactive system that may have played a central role in the evolution of language.