Social cognition is a topic of enormous interest and much research, but we are far from having an agreed taxonomy or factor structure of relevant processes. The aim of this review is to outline briefly what is known about the structure of social cognition and to suggest how further progress can be made to delineate the in(ter)dependence of core sociocognitive processes. We focus in particular on several processes that have been discussed and tested together in typical and atypical (notably autism spectrum disorder) groups: imitation, biological motion, empathy, and theory of mind. We consider the domain specificity/generality of core processes in social learning, reward, and attention, and we highlight the potential relevance of dual-process theories that distinguish systems for fast/automatic and slow/effortful processing. We conclude with methodological and conceptual suggestions for future progress in uncovering the structure of social cognition.