Using quantile regression techniques, we study the drivers of inflation risks in a large panel of advanced and emerging market economies (EMEs). We document several facts regarding the inflation forecast distribution and highlight some key differences between these two groups of countries. First, the exchange rate has a quantitatively important and non-linear impact on the inflation outlook in EMEs: a depreciation is associated with larger increases in the upper quantiles than in the lower quantiles, increasing the right skewness of the distribution. By contrast, there is no evidence of such non-linearities for advanced economies. Second, tighter financial conditions in EMEs carry both downside and upside risks to inflation, while having a muted impact on the modal or mean outcome. This is in contrast to advanced economies, where only downside risks prove sensitive. Third, the zero lower bound on policy rates translates into substantial downside risks to inflation. Finally, the adoption of inflation targeting is associated not only with lower mean inflation but also with a less right-skewed distribution. Our findings underscore the importance of including non-linearities in structural models of inflation dynamics.