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Inequality is important, both for its own sake and for its political, social, and economic implications. However, measuring inequality is not straightforward, as it requires decisions to be made on the variable, population, and distributional characteristics of interest. These decisions will naturally influence the conclusions that are drawn so they must be closely linked to an underlying purpose, which is ultimately defined by a social welfare function. This paper outlines important considerations when making each of these decisions, before surveying recent advances in measuring inequality and suggesting avenues for future work.