Payments systems play a fundamental role in an economy by providing the mechanisms through which payments arising from transactions can be settled. The existing literature on the economics of payments systems is large but loosely organized, in that each model uses a distinct set-up and sometimes a distinct equilibrium concept. As a result, it is not easy to generalize how model features are related to model implications. The authors conduct a non-technical survey of the literature and discuss some of these connections. They organize the literature according to three general classes of modelling approaches, and compare those approaches in terms of their strengths and weaknesses. They also describe the policy implications across the three model classes and relate them to the model environment/assumptions. The authors summarize what can be learned from the literature with respect to policy issues and identify areas for future research.