Beyond the MSSM

To increase the predictivity of the Minimal Supersymmetric Standard Model (MSSM), one needs to go to an underlying, more fundamental theory, where at least some of the many MSSM parameters can be determined by symmetries or by dynamics. Progress may come from four-dimensional superstring solutions and their effective supergravities. Summarizing some recent work, we introduce a class of `large-hierarchy-compatible' (LHC) models that could naturally embed a stable hierarchy m_Z ~ m_{3/2} << \mpl. We discuss how in LHC models one may determine: 1) the explicit mass terms of the MSSM, as functions of the gravitino mass; 2) the scales of gauge and supersymmetry breaking, m_Z and m_{3/2}; 3) the heavy-fermion masses. Based on talks given at: the Second IFT Workshop on Yukawa Couplings, Gainesville, Florida, USA, 11--13 February 1994; the XXIXth Rencontres de Moriond, M\'eribel, France, 12--19 March 1994; the First International Conference on Phenomenology of Unification from Present to Future, Rome, Italy, 23--26 March 1994.