This review considers computational psychiatry from a particular viewpoint: namely, a commitment to explaining psychopathology in terms of pathophysiology. It rests on the notion of a generative model as underwriting (i) sentient processing in the brain, and (ii) the scientific process in psychiatry. The story starts with a view of the brain-from cognitive and computational neuroscience-as an organ of inference and prediction. This offers a formal description of neuronal message passing, distributed processing and belief propagation in neuronal networks; and how certain kinds of dysconnection lead to aberrant belief updating and false inference. The dysconnections in question can be read as a pernicious synaptopathy that fits comfortably with formal notions of how we-or our brains-encode uncertainty or its complement, precision. It then considers how the ensuing process theories are tested empirically, with an emphasis on the computational modelling of neuronal circuits and synaptic gain control that mediates attentional set, active inference, learning and planning. The opportunities afforded by this sort of modelling are considered in light of in silico experiments; namely, computational neuropsychology, computational phenotyping and the promises of a computational nosology for psychiatry. The resulting survey of computational approaches is not scholarly or exhaustive. Rather, its aim is to review a theoretical narrative that is emerging across subdisciplines within psychiatry and empirical scales of investigation. These range from epilepsy research to neurodegenerative disorders; from post-traumatic stress disorder to the management of chronic pain, from schizophrenia to functional medical symptoms.