We examine how inflation risks have changed over time in a large panel of advancedand emerging market economies (EMEs). Quantile regressions show a general declinein upside inflation risks over time, reflecting successful disinflationary processes andthe adoption of inflation targeting regimes. But important non-linearities remain. Inadvanced economies, the zero lower bound represents a prominent source ofdownside inflation risk. In EMEs, the exchange rate remains a powerful source of nonlinearity,with large exchange rate depreciations associated with upside inflation risks.Tightening financial conditions increase both up- and downside inflation risks.Keywords: inflation risk; monetary policy framework; zero lower bound; inflationtargeting.