  This is a survey on Reidemeister torsion for hyperbolic three-manifolds of
finite volume. Torsions are viewed as topological invariants and also as
functions on the variety of representations in $\operatorname{ SL}_2(\mathbb
C)$. In both cases, the torsions may also be computed after composing with
finite dimensional representations of $\operatorname{ SL}_2(\mathbb C)$. In
addition the paper deals with the torsion of the adjoint representation as a
function on the variety of $\operatorname{ PSL}_{n+1}(\mathbb C)$-characters,
using that the first cohomology group with coefficients twisted by the adjoint
is the tangent space to the variety of characters.
