In this talk I will discuss recent results about the torsion
in the cohomology of arithmetic groups with coefficients in
${\mathbb Z}$-modules. One of the goals is to determine the growth of the
torsion if the rank of the ${\mathbb Z}$-module tends to infinity. In many
cases it grows exponentially with exponent proportional to the covolume.
The method is analytic and is based on the study of the Reidemeister torsion of
the locally symmetric space associated to the arithmetic group. If time
permits I will also discuss related results of Bergeron and Venkatesh, who
study the opposite case where the module is fixed and the group runs through
a family of congruence subgroups.

[invited by R. Kellerhals]