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Inflation persists at moderate rates of 15-30 percent in all the countries that successfully reduced triple digit inflations in the 1980s. Several other countries, for example Colombia, have experienced moderate inflation for prolonged periods. In this paper we first set out theories of persistent inflation, which can be classified into those emphasizing seigniorage as a source of government finance and those that emphasize the costs of ending inflation. We then examine the sources and persistence of moderate inflation episodes. Most were triggered by commodity price shocks; they were brief; and very few ended in higher inflation. We then present case studies of eight countries, including three that now suffer from moderate inflation, and four that successfully moved down to single digit inflation rates. We examine the roles of seigniorage, indexation and disindexation, the exchange rate commitment, and monetary and fiscal policy. The evidence suggests that seigniorage plays at most a modest role in the persistence of moderate inflations, and that such inflations can be reduced only at a substantial short-term cost to growth.