This paper examines the evidence that delusions can be explained within the framework of a neurocognitive model of how the brain assesses certainty. Here, 'certainty' refers to both low-level interpretations of one's environment and high-level (conscious) appraisals of one's beliefs and experiences. A model is proposed explaining how the brain systems responsible for assigning certainty might dysfunction, contributing to the cause and maintenance of delusional beliefs. It is suggested that delusions arise through a combination of perturbed striatal dopamine and aberrant salience as well as cognitive biases such as the tendency to jump to conclusions (JTC) and hypersalience of evidence-hypothesis matches. The role of emotion, stress, trauma and sociocultural factors in forming and modifying delusions is also considered. Understanding the mechanisms involved in forming and maintaining delusions has important clinical implications, as interventions that improve cognitive flexibility (e.g. cognitive remediation therapy and mindfulness training) could potentially attenuate neurocognitive processes.