Tetrachoric correlations are applied to estimate the relationships between continuous variables that underlie observed dichotomous/binary variables. Are they still relevant and useful for today's research in both the social and hard sciences?
For what it's worth, my graduate school statistics professors did teach tetrachoric correlation, but mostly so we would know what was going on when we encountered articles using the method. The sense was that this approach often inflates the "real" correlation, or at least provides a higher estimate than the nearly universally familiar Pearson-based methods, which will be misleading to most readers (who don't realize you've done something a bit idiosyncratic).