Rules governing human behaviour are at the heart of every system of natural resource management. Without compliance, however, rules are meaningless so effective enforcement is essential if conservation is to be successful. There is a large body of theory concerning enforcement and compliance with rules spread over several disciplines, including psychology, economics and sociology. However, there have been few attempts to extend this theory to conservation applications and there is little practical guidance for managers and conservation planners on the optimal design of enforcement programmes. We review approaches to understanding why individuals break rules and how optimal policy choices can reduce rule-breaking, highlighting research which has specifically dealt with natural resources. Because of the difficulty of studying rule-breaking behaviour directly, modelling approaches have been particularly important and have been used to explore behaviour at the individual, group and institutional levels. We illustrate the application of models of enforcement and compliance to conservation using the African elephant Loxodonta africana as a case study. Further work is needed to create practical tools which can be applied to the design of enforcement measures in conservation. Particular challenges include understanding the importance of violations of rationality assumptions and incorporating intertemporal choice in models of decision making. In conclusion, we argue that a new field of robust theory and practice is urgently needed to ensure that issues of enforcement and compliance do not undermine conservation initiatives.