I review the state of the art of the academic theoretical and empirical literature on the potential trade-off between competition and stability in banking. There are two basic channels through which competition may increase instability: by exacerbating the coordination problem of depositors/investors on the liability side and fostering runs/panics, and by increasing incentives to take risk and raise failure probabilities. The competition-stability trade-off is characterized and the implications of the analysis for regulation and competition policy are derived. It is found that optimal regulation may depend on the intensity of competition.