The diversity of cognitive deficits and neuropathological processes associated with dementias has encouraged divergence in pathophysiological explanations of disease. Here, we review an alternative framework that emphasizes convergent critical features of cognitive pathophysiology. Rather than the loss of 'memory centres' or 'language centres', or singular neurotransmitter systems, cognitive deficits are interpreted in terms of aberrant predictive coding in hierarchical neural networks. This builds on advances in normative accounts of brain function, specifically the Bayesian integration of beliefs and sensory evidence in which hierarchical predictions and prediction errors underlie memory, perception, speech and behaviour. We describe how analogous impairments in predictive coding in parallel neurocognitive systems can generate diverse clinical phenomena, including the characteristics of dementias. The review presents evidence from behavioural and neurophysiological studies of perception, language, memory and decision-making. The reformulation of cognitive deficits in terms of predictive coding has several advantages. It brings diverse clinical phenomena into a common framework; it aligns cognitive and movement disorders; and it makes specific predictions on cognitive physiology that support translational and experimental medicine studies. The insights into complex human cognitive disorders from the predictive coding framework may therefore also inform future therapeutic strategies.