Religions are evolutionary selected social and cultural phenomena. They represent today belief and normative systems on which the main parts of our culture are based. For a long time religions have been seen as mainly originating from a spectrum of religious experiences. These include a broad spectrum of experiences and are astonishingly widespread in the population. The most consistent and transculturally uniform religious experiences are the mystical experiences. Only these (and the prayer experience) have factually been researched in detail neurobiologically. This article presents a review of empirical results and hypothetical approaches to explain mystical religious experiences neurobiologically. Some of the explanatory hypotheses possess logical evidence, some are even supported by neurobiological studies, but all of them have their pitfalls and are at best partially consistent. One important insight from the evidence reviewed here is that there may be a whole array of different neurophysiological conditions which may result in the same core religious mystical experiences.