Epilepsy is a common and debilitating neurological disease. When medication cannot control seizures in up to 40% of cases, surgical resection of epileptogenic tissue is a clinically and cost- effective therapy to achieve seizure freedom. To simultaneously resect minimal yet sufficient cortex, exquisite localization of the epileptogenic zone (EZ) is crucial. However, localization is not straightforward, given relative difficulty of capturing seizures, constraints of the inverse problem in source localization, and possible disparate locations of symptomatogenic vs. epileptogenic regions. Thus, attention has been paid to which state of vigilance best localizes the EZ, in the hopes that one or another sleep-wake state may hold the key to improved accuracy of localization. Studies investigating this topic have employed diverse methodologies and produced diverse results. Nonetheless, rapid eye movement sleep (REM) has emerged as a promising sleep-wake state, as epileptic phenomena captured in REM may spatially correspond more closely to the EZ. Cortical neuronal asynchrony in REM may spatially constrain epileptic phenomena to reduce propagation away from the source generator, rendering them of high localizing value. However, some recent work demonstrates best localization in sleep-wake states other than REM, and there are reports of REM providing clearly false localization. Moreover, synchronistic properties and basic mechanisms of human REM remain to be fully characterized. Amidst these uncertainties, there is an urgent need for recording and analytical techniques to improve accuracy of localization. Here we present a systematic review and quantitative analysis of pertinent literature on whether and how REM may help localize epileptogenic foci. To help streamline and accelerate future work on the intriguing anti-epileptic properties of REM, we also introduce a simple, conceptually clear set-theoretic framework to conveniently and rigorously describe the spatial properties of epileptic phenomena in the brain.