The paper gives an overview over issues concerning the role of financial stability in monetary policy. Historically, financial stability has figured highly among central banks’ objectives, with policy measures ranging from interest rate stabilization to serving as a lender of the last resort. With the ascent of macroeconomics, these traditional tasks of central banks have been displaced by macroeconomic objectives, price stability, full employment, growth. The financial crisis has shifted the focus back to financial stability concerns. Along with these developments, the shift from a specie standard to a pure fiat money system has widened the scope for central bank policies, which are no longer constrained by legal obligations attached to central bank money. The paper first surveys the evolution of financial-stability and macroeconomic-stability concerns in central banking and monetary policy. Then it discusses two major challenges: (i) What should be done to assess the relevance of financial stability concerns in any given situation? How should one deal with the fact that systemic interdependence takes multiple forms and is changing all the time and that many contagion risks cannot be measured? (ii) What is the relation between financial-stability and macroeconomic-stability objectives? To what extent do they coincide, to what extent are they in conflict? How should tradeoffs be handled and what can be done to reduce the risk of the central bank’s succumbing to financial dominance?