We analyze inflation persistence in several industrial and emerging countries in the recent past by implementing unit root tests in the presence of unknown structural breaks and by estimating reduced-form models of inflation dynamics. We select a very representative group of 23 industrial and 17 emerging economies. Our sample period is comprised of quarterly data and differs for each country. Our results indicate that inflation persistence is decreasing over time for the great majority of industrial economies. Many emerging economies, however, show increasing persistence and even a few have highly persistent inflationary processes. We also observe structural breaks in all inflation processes we study with the exception of the inflation processes of Germany and Austria. Our results are robust to different reduced forms of the inflation processes and different econometric techniques.