What is Rank correlation, Spearman’s rho, Kendall’s tau?

A rank correlation measures dependence through the ranks of the observations only, so that it is unchanged by increasing transformations of either variable. Spearman’s rank correlation is the correlation of the ranks. Kendall’s tau is the probability that two independent pairs are concordant minus the probability that they are discordant, $\tau = \E[\operatorname{sign}((X - X')(Y - Y'))]$.