We want to conduct some meaningful and fruitful econometric research into multiple-output regression quantiles and related concepts of nonparametric statistics. In particular, we intend (a) to explore the use of directional and elliptical (regression) quantiles for statistical inference, (b) to generalize the elliptical (regression) quantiles in a few ways, (c) to overcome related computational issues and to implement elliptical quantile regression in a suitable software environment, and (d) to illustrate possible application of new methods.