Ageing populations in advanced economies are placing ever-increasing demands on government spending in the form of old-age benefits, particularly for health care. Economies that have promised substantially more benefits than they have made provision to finance are heading into a prolonged era of fiscal stress. Unresolved fiscal stress raises the possibility that the economies will hit their fiscal limits where taxes and spending no longer adjust to stabilise debt. In such economies, monetary policy may lose its ability to control inflation and influence the economy in the usual ways. The paper discusses models of fiscal limits and their implications and lays out a research agenda to integrate political economy and empirical considerations with general equilibrium models of monetary and fiscal interactions.