  Simple correlation coefficients between two variables have been generalized
to measure association between two matrices in many ways. Coefficients such as
the RV coefficient, the distance covariance (dCov) coefficient and kernel based
coefficients have been adopted by different research communities. Scientists
use these coefficients to test whether two random vectors are linked. If they
are, it is important to uncover what patterns exist in these associations.
  We discuss the topic of measures of dependence between random vectors and
tests of independence and show links between different approaches. We document
some of the interesting rediscoveries and lack of interconnection between
bodies of literature. After providing definitions of the coefficients and
associated tests, we present the recent improvements that enhance their
statistical properties and ease of interpretation. We summarize multi-table
approaches and provide scenarii where the indices can provide useful summaries
of heterogeneous multi-block data.
  We illustrate these different strategies on several examples of real data and
suggest directions for future research.
