After a long period of global price stability, in 2008 inflation increased sharply following unprecedented increases in the price of oil and other commodities, notably food. Although inflation remained lower and growth higher in inflation targeting countries than elsewhere, almost everywhere price stability seemed in jeopardy as consumer prices kept surging and central banks struggled to maintain expectations anchored. The rapid drop in energy and food prices that later accompanied the world slowdown helped avert the worse, but inflation stayed high in many inflation targeting countries. This paper uses a small open-economy DSGE model to design the correct monetary policy response to a protracted supply shock of the kind observed today, and explains how to choose optimal policy horizons under such shock. Using a version of the model with Kalman learning, the paper also evaluates the implications of a loss of target credibility, showing how rules must be adjusted when the authorities' commitment to low inflation has been eroded. The appropriate response to future evolutions of the price of oil, including to a large downward correction as recently observed, is also evaluated.