People with epilepsy are at heightened risk of sudden death compared to the general population. The leading cause of epilepsy-related premature mortality is sudden unexpected death in epilepsy (SUDEP). Postmortem investigation of people with SUDEP, including histological and toxicological analysis, does not reveal a cause of death, and the mechanisms of SUDEP remain largely unresolved. In this review we present the possible mechanisms underlying SUDEP, including respiratory dysfunction, cardiac arrhythmia and postictal generalized electroencephlogram suppression. Emerging studies in humans and animal models suggest there may be an underlying genetic basis to SUDEP in some cases. We will highlight a mounting body of evidence for the involvement of genetic risk factors in SUDEP, with a particular focus on the role of cardiac arrhythmia genes in SUDEP.