Central bankers frequently emphasize the critical importance of anchoring private inflation expectations for successful monetary policy and macroeconomic stabilization. In most monetary policy models, however, expectations are already anchored through the assumption of rational expectations and perfect knowledge of the economy. In this Paper, we re-examine the role of inflation expectations by positing, instead, that agents have imperfect knowledge of the precise structure of the economy and policy-makers' preferences, and rely on a perpetual learning technology to form expectations. We find that with learning, disturbances can give rise to endogenous inflation scares, that is, significant and persistent deviations of inflation expectations from those implied by rational expectations, even at long horizons. The presence of learning increases the sensitivity of inflation expectations and the term structure of interest rates to economic shocks, in line with the empirical evidence. We also explore the role of private inflation expectations for the conduct of efficient monetary policy. Under rational expectations, inflation expectations equal a linear combination of macroeconomic variables and as such provide no additional information to the policy-maker. In contrast, under learning, private inflation expectations follow a time-varying process and provide useful information for the conduct of monetary policy.