There has been a recent explosion in research applying Bayesian models to cognitive phenomena. This development has resulted from the realization that across a wide variety of tasks the fundamental problem the cognitive system confronts is coping with uncertainty. From visual scene recognition to on-line language comprehension, from categorizing stimuli to determining to what degree an argument is convincing, people must deal with the incompleteness of the information they possess to perform these tasks, many of which have important survival-related consequences. This paper provides a review of Bayesian models of cognition, dividing them up by the different aspects of cognition to which they have been applied. The paper begins with a brief review of Bayesian inference. This falls short of a full technical introduction but the reader is referred to the relevant literature for further details. There follows reviews of Bayesian models in Perception, Categorization, Learning and Causality, Language Processing, Inductive Reasoning, Deductive Reasoning, and Argumentation. In all these areas, it is argued that sophisticated Bayesian models are enhancing our understanding of the underlying cognitive computations involved. It is concluded that a major challenge is to extend the evidential basis for these models, especially to accounts of higher level cognition. WIREs Cogn Sci 2010 1 811-823 For further resources related to this article, please visit the WIREs website.