Research has shown that the brain is constantly making predictions about future events. Theories of prediction in perception, action and learning suggest that the brain serves to reduce the discrepancies between expectation and actual experience, i.e., by reducing the prediction error. Forward models of action and perception propose the generation of a predictive internal representation of the expected sensory outcome, which is matched to the actual sensory feedback. Shared neural representations have been found when experiencing one's own and observing other's actions, rewards, errors, and emotions such as fear and pain. These general principles of the "predictive brain" are well established and have already begun to be applied to social aspects of cognition. The application and relevance of these predictive principles to social cognition are discussed in this article. Evidence is presented to argue that simple non-social cognitive processes can be extended to explain complex cognitive processes required for social interaction, with common neural activity seen for both social and non-social cognitions. A number of studies are included which demonstrate that bottom-up sensory input and top-down expectancies can be modulated by social information. The concept of competing social forward models and a partially distinct category of social prediction errors are introduced. The evolutionary implications of a "social predictive brain" are also mentioned, along with the implications on psychopathology. The review presents a number of testable hypotheses and novel comparisons that aim to stimulate further discussion and integration between currently disparate fields of research, with regard to computational models, behavioral and neurophysiological data. This promotes a relatively new platform for inquiry in social neuroscience with implications in social learning, theory of mind, empathy, the evolution of the social brain, and potential strategies for treating social cognitive deficits.