Studying psychiatric illness has often been limited by difficulties in connecting symptoms and behavior to neurobiology. Computational psychiatry approaches promise to bridge this gap by providing formal accounts of the latent information processing changes that underlie the development and maintenance of psychiatric phenomena. Models based on these theories generate individual-level parameter estimates which can then be tested for relationships to neurobiology. In this review, we explore computational modelling approaches to one key aspect of health and illness: affect. We discuss strengths and limitations of key approaches to modelling affect, with a focus on reinforcement learning, active inference, the hierarchical gaussian filter, and drift-diffusion models. We find that, in this literature, affect is an important source of modulation in decision making, and has a bidirectional influence on how individuals infer both internal and external states. Highlighting the potential role of affect in information processing changes underlying symptom development, we extend an existing model of psychosis, where affective changes are influenced by increasing cortical noise and consequent increases in either perceived environmental instability or expected noise in sensory input, becoming part of a self-reinforcing process generating negatively valenced, over-weighted priors underlying positive symptom development. We then provide testable predictions from this model at computational, neurobiological, and phenomenological levels of description.