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Despite representing the leading cause of epilepsy-related mortality, the pathophysiology of sudden unexpected death in epilepsy (SUDEP) remains elusive. In this context, the identification of clinical markers of SUDEP assumes a great importance and has been the target of many studies aimed at stratifying patients' individual risk. Among the potentially most hazardous post-ictal phenomena observed following convulsive seizures in monitored SUDEP cases, postictal generalized EEG suppression and postictal immobility have attracted attention as potential SUDEP risk factors. In this manuscript, we review the current knowledge on postictal generalized EEG suppression and postictal immobility, aiming to identify their pathophysiological mechanisms, reported frequencies and associated clinical factors, and critically evaluate the evidence on their potential relevance as SUDEP risk markers.