Humans cooperate with a striking array of partners on activities that range from moving furniture to combating global climate change. Typically, our cooperative behavior and psychology have been investigated using ‘social dilemma models’ that examine how people cooperate in the face of personal temptations to ‘free ride’ (to reap the benefits of others’ cooperation without investing substantially). Another model, known as the ‘coordination problem’, examines how cooperative action can emerge when it is in the strategic interests of all, but requires convergence on one of multiple cooperative solutions. A series of experiments will be summarized that investigate the behavior of children and our closest evolutionary relatives, chimpanzees, in coordination problems. Main results will point to striking similarities, as well as species-divergence, in evolved coordination capacities. The social-cognitive mechanisms utilized by children to coordinate will then be explored in more detail with reference to, for example, Theory of Mind, different types of communication, and social group identity. This is intended to provide some traction on the problem of how human cooperation has become conventionalized and institutionalized over evolutionary history.