  This survey article is an introduction to some of Lusztig's work on the
character theory of a finite group of Lie type $G(F_q)$, where $q$ is a power
of a prime~$p$. It is partly based on two series of lectures given at the
Centre Bernoulli (EPFL) in July 2016 and at a summer school in Les Diablerets
in August 2015. Our focus here is on questions related to the parametrization
of the irreducible characters and on results which hold without any assumption
on~$p$ or~$q$.
