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Simple correlation coefficients between two variables have been generalizedto measure association between two matrices in many ways. Coefficients such asthe RV coefficient, the distance covariance (dCov) coefficient and kernel basedcoefficients have been adopted by different research communities. Scientistsuse these coefficients to test whether two random vectors are linked. If theyare, it is important to uncover what patterns exist in these associations.  We discuss the topic of measures of dependence between random vectors andtests of independence and show links between different approaches. We documentsome of the interesting rediscoveries and lack of interconnection betweenbodies of literature. After providing definitions of the coefficients andassociated tests, we present the recent improvements that enhance theirstatistical properties and ease of interpretation. We summarize multi-tableapproaches and provide scenarii where the indices can provide useful summariesof heterogeneous multi-block data.  We illustrate these different strategies on several examples of real data andsuggest directions for future research.

Measures of dependence between random vectors and tests of independence. Literature review