  During the past three decades fundamental progress has been made on
constructing large torsion-free subgroups (i.e. subgroups of finite index) of
the unit group $\U (\Z G)$ of the integral group ring $\Z G$ of a finite group
$G$. These constructions rely on explicit constructions of units in $\Z G$ and
proofs of main results make use of the description of the Wedderburn components
of the rational group algebra $\Q G$. The latter relies on explicit
constructions of primitive central idempotents and the rational representations
of $G$. It turns out that the existence of reduced two degree representations
play a crucial role. Although the unit group is far from being understood, some
structure results on this group have been obtained. In this paper we give a
survey of some of the fundamental results and the essential needed techniques.
