This paper considers a number of different measures of core inflation and tries to identify those containing the most useful information about future movements in headline inflation rates over the horizons relevant for monetary policy for the United States, the euro area, Japan, the United Kingdom and Canada. The paper shows that the adjusted indicators do considerably better than the headline rate at determining the underlying inflation trend and, being considerably less volatile, can also be used at higher frequencies to provide more timely information. Most of these indicators also contain information relevant to predicting future headline inflation and which is additional to that contained in the headline rate. However, the relative performance of different indicators varies considerably across economies, and in some cases across sample periods. There is evidence that headline inflation tends to converge toward core inflation over time horizons of between 12 and 24 months. However, the estimated model incorporating this relationship between headline and core inflation does rather poorly in out-of-sample tests, althoughout-of-sample performance is much better for other specifications.