Bayesian decision theory can be used to model animal behaviour. In this paper we give an overview of the theoretical concepts in such models. We also review the biological contexts in which Bayesian models have been applied, and outline some directions where future studies would be useful. Bayesian decision theory, when applied to animal behaviour, is based on the assumption that the individual has some sort of "prior opinion" of the possible states of the world. This may, for example, be a previously experienced distribution of qualities of food patches, or qualities of potential mates. The animal is then assumed to be able use sampling information to arrive at a "posterior opinion", concerning e.g. the quality of a given food patch, or the average qualities of mates in a year. A correctly formulated Bayesian model predicts how animals may combine previous experience with sampling information to make optimal decisions. We argue that the assumption that animals may have "prior opinions" is reasonable. Their priors may come from one or both of two sources: either from their own individual experience, gained while sampling the environment, or from an adaptation to the environment experienced by previous generations. This means that we should often expect to see "Bayesian-like" decision-making in nature.