We review what the standard approach and a number of nonstandard approaches to game theory say about what rational agents should do, should believe about others’ actions and beliefs, and can expect to attain when they interact with other rational and not rational agents. We address these questions from the point of view of the standard approach, which is based on the postulate of best-response reasoning, and discuss how a number of alleged shortcomings of the standard approach have been proposed to be remedied by the theories of Pareto optimization, team reasoning, and virtual bargaining. We consider the case for dropping the fundamental but often problematic assumption of common belief in rationality. In the context of simultaneous-move games, we discuss the theory of level-k reasoning, and in the context of sequential-move games, we review recent developments in epistemic game theory.