George Lusztig has made profound and extensive contributions to the theory of linear representations of finite groups of Lie type. His explicit constructions using powerful geometric and topological methods have led to very complete and detailed results, including precise character formulae. For many years, he has been at the centre of the remarkable resurgence of international activity in this area. In addition, his joint discovery of the Kazhdan–Lusztig polynomials has been the main stimulus behind recent fundamental developments in the area between algebra, geometry and analysis.