In 1991, the rate of inflation in the Czech Republic, Hungary and Poland was between 35% and 70%. At the end of 2001, it is below 8%. We setup a small structural macro model of these economies to explain the process of disinflation. Contrary to a widespread skepticism, which permeated a large part of previous research on these issues, we show that a simple open macroeconomic model, along the lines of Svensson (2000, Journal of International Economics), with forward-looking inflation and exchange rate expectations, can adequately characterize the relationship between the output gap, inflation, the real interest rate and the exchange rate during the course of transition. We use the estimated models to interpret the main features of monetary policy in each country and identify the channels of policy transmission. We characterize the policy rules and assess the relative importance of the interest rate channel (on aggregate demand) and the exchange rate channel (which affects both aggregate demand and supply) in determining the path of (dis)inflation. In the same context, we also tentatively analyze the consequences of attempting a faster path of disinflation. Finally, we evaluate the appropriateness of the inflation targeting framework which has been adopted recently in all three countries, and discuss to what extent it represents a discontinuity with the past.