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.Comment: 12 A4-pages, no figures (to be LATEXed twice), preprint
CERN-TH.7325/9
