Summary: The aim of this paper is to survey and investigate the properties of the extended Gini family of inequality measures. The paper surveys the alternative ways of spelling the extended Gini for continuous distributions (such as via covariance, via Lorenz curves, etc.), and the metrics that motivate them. It also offers the adjustments needed for consistent estimation in the case of discrete distributions. The relationship between the family and welfare dominance is discussed. Then, the equivalent parameters to the covariance and correlations that are required for the decomposition of a sum of random variables into the contribution of components are defined, and the new frontiers it opens for estimating a regression based on those measures is illustrated. Finally, the implications of analyzing the effect of policies intended to change the income distribution are discussed.