In this article I develop a big picture of the evolution of human cooperation, and contrast it to an alternative based on group selection. The crucial claim is that hominin history has seen two major transitions in cooperation, and hence poses two deep puzzles about the origins and stability of cooperation. The first is the transition from great ape social lives to the lives of Pleistocene cooperative foragers; the second is the stability of the social contract through the early Holocene (...) transition to complex hierarchical societies. The first of these transitions is driven, at least initially, by individual advantage: cooperation paid off for individual foragers, initially through mutualist interaction, then through reciprocation. This argument leads to a reanalysis of the role of violence and the nature of the freeriding threat to cooperation. But the conditions that select for cooperative individuals in the Pleistocene were eroded in the Pleistocene–Holocene transition. So we need an alternative account of the survival, and indeed the expansion, of cooperation in the Holocene. Group selection driven by intercommunal conflict really may well be central to this second transition. (shrink)