SummarySeveral brainstem, subcortical and cortical areas are involved in the generation of rapid eye movement (REM) sleep. The alteration of these structures as a result of a neurodegenerative process may therefore lead to REM sleep anomalies. REM sleep behaviour disorder is associated with nightmares, dream‐enacting behaviours and increased electromyographic activity in REM sleep. Its isolated form is a harbinger of synucleinopathies such as Parkinson's disease or dementia with Lewy bodies, and neuroprotective interventions are advocated. This link might also be present in patients taking antidepressants, with post‐traumatic stress disorder, or with a history of repeated traumatic head injury. REM sleep likely contributes to normal memory processes. Its alteration has also been proposed to be part of the neuropathological changes occurring in Alzheimer's disease.