This paper provides a review of the concept of core inflation and evaluates the performance of several proposed measures. We first consider the rationale of a central bank in setting its inflation goal in terms of a selected rate of consumer price growth and the use of a core inflation measure as a means of achieving this long-term policy objective. We then discuss desired attributes of a core measure of inflation, such as ease of design, accuracy in tracking trend inflation, and predictive content for future movements in aggregate inflation. Using these attributes as criteria, we evaluate several candidate series that have been proposed as core measures of consumer price index (CPI) inflation and personal consumption expenditure (PCE) inflation for the United States. The candidate series are inflation excluding food and energy, inflation excluding energy, and median inflation, as well as exponentially smoothed versions of aggregate inflation and the aforementioned individual series. ; For PCE inflation, we examine quarterly data starting in 1959. Unlike previous research, we confine our analysis to the methodologically consistent CPI index, which is only available starting in 1978. We find that most of the candidate series, including the familiar ex-food and energy measure, demonstrate the ability to match the mean rate of aggregate inflation and track movements in its underlying trend. In the within-sample analysis, we find that core measures derived through exponential smoothing, in combination with simple measures of economic slack, have substantial explanatory content for changes in aggregate inflation several years in advance. In the out-of-sample analysis, however, we find that no measure performs consistently well in forecasting inflation. Moreover, we document evidence of some parameter instability in the estimated forecasting models. Taken together, our findings lead us to conclude that there is no individual measure of core inflation that can be considered superior to other measures.