Inflation targeting (IT) had originally been introduced as a device to bring inflation down and stabilize it at low levels. Given the current environment of persistently weak inflation in many advanced economies, IT central banks must now bring inflation up to target. In this paper, the author tests to what extent inflation expectations are anchored in such circumstances, by comparing (i) IT and non-IT countries, and (ii) across periods when inflation is at normal levels, (persistently) high, or (persistently) weak. He finds that under low and persistently low inflation, some disanchoring can occur - inflation expectations are more dependent on lagged inflation; forecasters tend to disagree more; and inflation expectations get revised down in response to lower-than-expected inflation, but do not respond to higher-than-expected inflation. Since inflation expectations in IT countries are substantially better anchored than those in the control group, policy rates in IT countries need to react less to changes in inflation, making IT central banks considerably less likely to hit the zero lower bound.