Although largely unaddressed by evolutionary theory for more than a century after Darwin, over the last decade a wide range of adaptationist, byproduct, and memetic explanations have emerged for various recurrent features of religious belief and practice. One feature that has figured prominently in adaptationist accounts of religion is belief in the reality of moralizing, punishing supernatural agents. However, there is at present no unified theory of what fitness-relevant feature of the selective environment to which this cognitive predisposition is adapted. We distinguish two divergent and often conflated approaches to supernatural punishment theory which hypothesize the adaptive character of such beliefs arise from the fact that they increase cooperation or decrease the cost of incurring punishment for norm violations. We evaluate these, and group and individual selectionist versions, in view of game theoretic models, experimental studies, and ethnographic data in light of which each proposal is plausible but with which none is fully concordant.