Which social decisions are intuitive? Which are deliberative? The dual-process approach to human sociality has emerged in the last decades as a vibrant and exciting area of research. Here, I review the existing literature on the cognitive basis of cooperation, altruism, honesty, positive and negative reciprocity, and (act) utilitarianism. I conclude by introducing a game-theoretical framework that organizes the majority of the empirical regularities. This framework extends Rand and colleagues’ Social Heuristics Hypothesis to any one-shot game G. The core assumption of this “General Social Heuristics Hypothesis” is that, under intuition, people play a Nash equilibrium of the “real analogue of G”, G^real, while under deliberation people play a Nash equilibrium of G. G^real differs from G along two dimensions: G is one-shot, while G^real might be iterated; the payoffs of G^real might be different from the payoffs of G, although they are ordered in (almost) the same way.