  We describe the main questions connected to torsion subgroups in the unit
group of integral group rings of finite groups and algorithmic methods to
attack these questions. We then prove the Zassenhaus Conjecture for Amitsur
groups and prove that any normalized torsion subgroup in the unit group of an
integral group of a Frobenius complement is isomorphic to a subgroup of the
group base. Moreover we study the orders of torsion units in integral group
rings of finite almost quasisimple groups and the existence of torsion-free
normal subgroups of finite index in the unit group.
