Bayesian theories have attracted enormous attention in the cognitive sciences in recent years. According to these theories, the mind assigns probabilities to hypotheses and updates them according to standard probabilistic rules of inference. Bayesian theories have been applied to the study of perception, learning, memory, reasoning, language, decision-making, and many other domains. Bayesian approaches have also become increasingly popular in neuroscience, and a number of potential neurobiological mechanisms have been proposed. At the same time, Bayesian theories raise many foundational questions, the answers to which have been controversial: Does the brain actually use Bayesian rules? Or are they merely approximate descriptions of behavior? How well can Bayesian theories accommodate irrationality in cognition? Do they require an implausibly uniform view of the mind? Are Bayesian theories near-trivial due to their many degrees of freedom? What are their implications for the relationship between perception, cognition, rationality, and consciousness?