The ability to coordinate our actions with those of others is crucial for our success as individuals and as a species. Progress in understanding the cognitive and neural processes involved in joint action has been slow and sparse, because cognitive neuroscientists have predominantly studied individual minds and brains in isolation. However, in recent years, major advances have been made by investigating perception and action in social context. In this article we outline how studies on joint attention, action observation, task sharing, action coordination and agency contribute to the understanding of the cognitive and neural processes supporting joint action. Several mechanisms are proposed that allow individuals to share representations, to predict actions, and to integrate predicted effects of own and others' actions.