  We consider the heterotic E8 X E8 string theory, which gives rise to
four-dimensional Standard-like Models and allows for their SO(10) embedding. We
investigate two different schemes of compactification: the free fermionic
formulation and the orbifold construction. In the examples presented in the
free fermionic formulation we explore the removal of the extra Higgs
representations by using the free fermion boundary conditions directly at the
string level, rather than in the effective low energy field theory. Moreover,
by employing the standard analysis of flat directions we present a
quasi-realistic three generation string model in which stringent F- and D- flat
solutions do not appear to exist to all orders in the superpotential. We show
that, by choosing a non-factorisable compactification lattice, defined by
skewing its standard simple roots, we decrease the total number of generations.
Finally, the construction of modular invariant partition functions for E8 X E8
orbifold compactifications is presented.
