The massive accumulation of international reserves in developing economies is one of the most puzzling recent developments in the world economy. This paper argues that it can be explained by a simple model in which the central bank smooths inflation and stabilizes the exchange rate. I explore the view that reserve accumulation is the consequence of an increase in the incidence and magnitude of banking crises. These crises impose exceptional costs that need to be financed with inflation related revenues. Inflation is distortionary. As a result, the central bank optimally accumulates international reserves in order to spread the distortions associated with inflation over time. A quantitative exercise for an average developing economy using data between 1970 and 2007 predicts long-run levels of reserves that coincide with average holdings in developing economies. Furthermore, the monetary perspective studied in this paper sheds light on the determinants of cross-sectional variation in reserve holdings.