Norms permeate human life. Most of people’s activities can be characterized by rules about what is appropriate, allowed, required, or forbidden—rules that are crucial in making people hyper-cooperative animals. In this article, I examine the current cognitive-evolutionary account of “norm psychology” and propose an alternative that is better supported by evidence and better placed to promote interdisciplinary dialogue. The incumbent theory focuses on rules and claims that humans genetically inherit cognitive and motivational mechanisms specialized for processing these rules. The cultural-evolutionary alternative defines normativity in relation to behavior—compliance, enforcement, and commentary—and suggests that it depends on implicit and explicit processes. The implicit processes are genetically inherited and domain-general; rather than being specialized for normativity, they do many jobs in many species. The explicit processes are culturally inherited and domain-specific; they are constructed from mentalizing and reasoning by social interaction in childhood. The cultural-evolutionary, or “cognitive gadget,” perspective suggests that people alive today—parents, educators, elders, politicians, lawyers—have more responsibility for sustaining normativity than the nativist view implies. People’s actions not only shape and transmit the rules, but they also create in each new generation mental processes that can grasp the rules and put them into action.