Explicit models of cultural and genetic dynamics can be used to sharpen intuitions and reveal counter-intuitive phenomena, and provide a framework for robust inference of past processes. Two of the most important cultural transitions in human evolution were the Upper Palaeolithic transition; sometimes called the origins of modern human behaviour, and the transition to sedentism and farming. Using cultural evolutionary models I will show how population density and connectivity are critical determinants of the accumulation and maintenance of skills and technologies that characterises the Upper Palaeolithic transition, and that farming was more likely to emerged in small, conservative groups, in association with property rights, but that increased productivity was not essential. Finally I will show how genetic data can be used to identify adaptations to changes in ecology and diet following the transition to farming.