This paper studies factors behind inflation dynamics in the euro area, the UK and the US. It introduces a factor-augmented vector autoregression (FAVAR) framework with sign restrictions to study the effects of fundamental macroeconomic shocks on inflation in the three economies. The FAVAR model framework is also applied to study the effects on inflation subcomponents in the more recent past. The FAVAR models suggest that headline inflation in the three economies has reacted in a relatively similar fashion to macroeconomic shocks over the last four decades, with demand shocks causing the most persistent effects on inflation. According to the subcomponent FAVAR models, the responses of inflation subcomponents to macroeconomic shocks have also been relatively similar in the three economies. However, there is evidence of a stronger foreign exchange channel of monetary policy transmission as well as supply shocks in the responses of non-energy tradable goods prices in the UK than the other two economies, while the reaction of services inflation has been more muted to all types of shocks in the euro area than the other two economies.