This paper argues that recent research on normal-belief formation is relevant to our understanding of the establishment and maintenance of delusions. Bayesian theory provides a normative model of the way in which evidence relevant to normal beliefs may be evaluated: this makes it possible to classify delusional beliefs in terms of deviations from optimal Bayesian inference. Some hypothetical forms of deviation appear to correspond closely to cognitive processes observed in some groups of deluded patients. Theories of the precise nature of the abnormal judgemental processes also have implications for psychological approaches to treatment of deluded patients. The role of hallucinations in the formation and/or maintenance of delusions and the extent to which the distortions of cognitive processes associated with delusions are content-specific or mood-specific are also considered.