This article reviews various approaches to the measurement of core inflation that have been proposed over the years using the stochastic approach to index numbers as a unifying framework. It begins with a review of how the concept of core inflation is used by the world’s major central banks, including some of the inflation-targeting central banks. The author provides a comprehensive review of many of the measures of core inflation that have been developed over the years and highlights some of the conceptual and practical problems associated with them.