  This thesis provides a classification of the chiral content of the heterotic
$\mathbbm{Z}_2 \times \mathbbm{Z}_2$ orbifold models. We show that the chiral
content of the heterotic $\mathbbm{Z}_2 \times \mathbbm{Z}_2$ orbifold models
at any point in the moduli space can be described by a free fermionic model. We
present a direct translation between the orbifold formulation and the free
fermionic construction. We use the free fermionic description for the
classification wherein we consider orbifolds with symmetric shifts.
  We show that perturbative three generation models are not obtained in the
case of $\mathbbm{Z}_2 \times \mathbbm{Z}_2$ orbifolds with symmetric shifts on
complex tori, and that the perturbative three generation models in this class
necessarily employ an asymmetric shift. We show that the freedom in the modular
invariant phases in the $N = 1$ vacua that control the chiral content, can be
interpreted as vacuum expectation values of background fields of the underlying
$N = 4$ theory, whose dynamical components are projected out by the
$\mathbbm{Z}_2$ fermionic projections. In this class of vacua the chiral
content of the models is determined by the underlying $N = 4$ mother theory.
