In this paper we take another look at the literature on central bank independence. We show that the representative-agent approach to monetary policy is seriously flawed and does not provide a sound basis for deriving institutional solutions to the inflationary-bias. We then argue that the political approach to monetary policy provides a better account of the inflationary-bias and that this has important implications for the set-up of institutional arrangements, like central-bank independence, and the role of contractual arrangements, like indexation. Central bank independence, if appropriately modeled, can fail to reduce inflationary pressures in plausible circumstances. We then identify some issues in the theory of central banking that have not been clearly resolved and we offer some intuition as to the way they could be studied. We conclude by showing some potentially worrisome implications for the future of the European Monetary Union.