We review an extensive literature debating the merits of alternative priority structures for banking liabilities put forward by financial economists, legal scholars and policymakers. Up to now, this work has focused exclusively on the relative advantages of each group of creditors to monitor the activities of bankers. We argue that systemic risk is another dimension that this discussion must include. The main message of our work is that when bank failures are contagious then when regulators assign priority rights need also to take into account how the bankruptcy resolution of one institution might affect the survival of other institutions that have acted as its creditors. When the network structure is fixed the solution is straightforward. Other banks should have priority to minimize the risk of their downfall. However, if the choice of policy can affect the structure of the network, policy design becomes more complex.This is a fruitful avenue for future research.