  These notes are based on a course given at the EPFL in May 2005. It is
concerned with the representation theory of Hecke algebras in the
non-semisimple case. We explain the role that these algebras play in the
modular representation theory of finite groups of Lie type and survey the
recent results which complete the classification of the simple modules. These
results rely on the theory of Kazhdan--Lusztig cells in finite Weyl groups
(with respect to possibly unequal parameters) and the theory of canonical bases
for representations of quantum groups.
