  We review the theory and phenomenology of effective supergravity theories
based on orbifold compactifications of the weakly-coupled heterotic string. In
particular, we consider theories in which the four-dimensional theory displays
target space modular invariance and where the dilatonic mode undergoes Kahler
stabilization. A self-contained exposition of effective Lagrangian approaches
to gaugino condensation and heterotic string theory is presented, leading to
the development of the models of Binetruy, Gaillard and Wu. Various aspects of
the phenomenology of this class of models are considered. These include issues
of supersymmetry breaking and superpartner spectra, the role of anomalous U(1)
factors, issues of flavor and R-parity conservation, collider signatures, axion
physics, and early universe cosmology. For the vast majority of
phenomenological considerations the theories reviewed here compare quite
favorably to other string-derived models in the literature. Theoretical
objections to the framework and directions for further research are identified
and discussed.
