In most OECD countries, we cannot reject up to three breaks in the mean of inflation: one break in the late 1960’s-early 1970’s, one in the early-mid 1980’s and another break in the early 1990’s. These breaks tend to be associated more often to breaks in the mean of nominal variables than to the one of real variables, which reinforces the view that they are monetary phenomena. We also show that ignoring breaks in the mean of inflation clearly lead to overrate inflation persistence in standard bi-variate models of inflation. The response of inflation to shocks in these models is markedly faster with breaks than without breaks. Finally, controlling for breaks in the mean of inflation weakens the effects on inflation of M3 growth and of the real unit labour cost towards insignificance while the effects of the output gaps on inflation are more robust.