Delusions are the false and often incorrigible beliefs that can cause severe suffering in mental illness. We cannot yet explain them in terms of underlying neurobiological abnormalities. However, by drawing on recent advances in the biological, computational and psychological processes of reinforcement learning, memory, and perception it may be feasible to account for delusions in terms of cognition and brain function. The account focuses on a particular parameter, prediction error – the mismatch between expectation and experience – that provides a computational mechanism common to cortical hierarchies, frontostriatal circuits and the amygdala as well as parietal cortices. We suggest that delusions result from aberrations in how brain circuits specify hierarchical predictions, and how they compute and respond to prediction errors. Defects in these fundamental brain mechanisms can vitiate perception, memory, bodily agency and social learning such that individuals with delusions experience an internal and external world that healthy individuals would find difficult to comprehend. The present model attempts to provide a framework through which we can build a mechanistic and translational understanding of these puzzling symptoms.