Information processing in the nervous system involves the activity of large populations of neurons. It is possible, however, to interpret the activity of relatively small numbers of cells in terms of meaningful aspects of the environment. 'Bayesian inference' provides a systematic and effective method of combining information from multiple cells to accomplish this. It is not a model of a neural mechanism (neither are alternative methods, such as the population vector approach) but a tool for analysing neural signals. It does not require difficult assumptions about the nature of the dimensions underlying cell selectivity, about the distribution and tuning of cell responses or about the way in which information is transmitted and processed. It can be applied to any parameter of neural activity (for example, firing rate or temporal pattern). In this review, we demonstrate the power of Bayesian analysis using examples of visual responses of neurons in primary visual and temporal cortices. We show that interaction between correlation in mean responses to different stimuli (signal) and correlation in response variability within stimuli (noise) can lead to marked improvement of stimulus discrimination using population responses.