Although largely neglected in earlier literature, sudden unexpected death in epilepsy (SUDEP) is the most important epilepsy-related mode of death, and is the leading cause of death in people with chronic uncontrolled epilepsy. Research during the past two to three decades has shown that incidence varies substantially depending on the epilepsy population studied, ranging from 0.09 per 1000 patient-years in newly diagnosed patients to 9 per 1000 patient-years in candidates for epilepsy surgery. Risk profiles have been delineated in case-control studies. These and other studies indicate that SUDEP mainly occurs in the context of a generalised tonic-clonic seizure. However, it remains unclear why a seizure becomes fatal in a person that might have had many similar seizures in the past. Here, we review SUDEP rates, risk factors, triggers, and proposed mechanisms, and critically assess potential preventive strategies. Gaps in knowledge are discussed and ways forward are suggested.