This paper introduces distance correlation as a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike classical correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on Euclidean distances between sample elements rather than sample moments, and have a compact representation similar to classical covariance and correlation. The paper discusses the asymptotic properties and applications of distance covariance in testing independence, and presents Monte Carlo results showing that the distance covariance test has superior power against nonmonotone types of dependence while maintaining good power performance in the multivariate normal case relative to the parametric likelihood ratio test. Distance correlation can also be used as an index of dependence, such as in meta-analysis, without requiring normality for valid inferences. Theoretical properties of distance covariance and correlation are covered in Section 2, extensions in Section 3, and results for the bivariate normal case in Section 4. Empirical results are presented in Section 5, followed by a summary in Section 6. The paper defines distance covariance and distance correlation, and shows that distance correlation satisfies 0 ≤ R ≤ 1, and R = 0 only if X and Y are independent. The paper also discusses the asymptotic properties of the distance covariance statistic, showing that under independence, nV_n² converges in distribution to a quadratic form. The paper also presents empirical results comparing the power of the distance covariance test with classical tests for multivariate independence, showing that the distance covariance test has superior power against nonmonotone types of dependence. The paper concludes that distance correlation is a useful measure of dependence that can be applied in a wide range of situations.This paper introduces distance correlation as a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike classical correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on Euclidean distances between sample elements rather than sample moments, and have a compact representation similar to classical covariance and correlation. The paper discusses the asymptotic properties and applications of distance covariance in testing independence, and presents Monte Carlo results showing that the distance covariance test has superior power against nonmonotone types of dependence while maintaining good power performance in the multivariate normal case relative to the parametric likelihood ratio test. Distance correlation can also be used as an index of dependence, such as in meta-analysis, without requiring normality for valid inferences. Theoretical properties of distance covariance and correlation are covered in Section 2, extensions in Section 3, and results for the bivariate normal case in Section 4. Empirical results are presented in Section 5, followed by a summary in Section 6. The paper defines distance covariance and distance correlation, and shows that distance correlation satisfies 0 ≤ R ≤ 1, and R = 0 only if X and Y are independent. The paper also discusses the asymptotic properties of the distance covariance statistic, showing that under independence, nV_n² converges in distribution to a quadratic form. The paper also presents empirical results comparing the power of the distance covariance test with classical tests for multivariate independence, showing that the distance covariance test has superior power against nonmonotone types of dependence. The paper concludes that distance correlation is a useful measure of dependence that can be applied in a wide range of situations.