Minimal Lagrangian submanifolds are most interesting when the ambient manifold is Kaehler-Einstein (KE). In the negative KE case, recent results (joint with J. Lotay, UCL) reveal several new features of minimal Lagrangians. In this seminar I will try to explain how these results point towards new research problems concerning the existence, uniqueness, topology and complex-analytic properties of minimal Lagrangians.