This paper provides a snapshot of the state of the literature on payment cards, particularly from the perspective of interchange fees and the economics literature on two-sided markets. The paper aims to integrate a wide range of theoretical papers with the relevant empirical research and important policy questions. Our point of difference compared to previous surveys is to focus on the relevant insights that come from theoretical models and what needs to be done to better connect this theory with the relevant policy issues. We address regulatory and competition policy justifications for intervention, as well as practical issues in implementation. Finally, we point to directions for new theoretical and empirical work to bridge the gap between economics and policy.