We provide a model that unifies the notion of self-fulfilling banking crises and sovereign debt crises. In this model, a bank run can be contagious by triggering a sovereign default, and vice versa. A deposit insurance scheme can eliminate the adverse equilibrium only if the government can repay its debt and credibly insure deposits irrespective of the performance of the financial sector. Moreover, we analyze how banking crises and sovereign defaults can be contagious across countries. We give conditions under which the implementation of a banking union is effective and costless. Finally, we discuss the current proposals for a banking union in the euro area and argue that it should be extended by a supranational Deposit Guarantee Scheme.