  This article is a survey on the cohomology of a reductive algebraic group
with coefficients in twisted representations. A large part of the paper is
devoted to the advances obtained by the theory of strict polynomial functors
initiated by Friedlander and Suslin in the late nineties. The last section
explains that the existence of certain `universal classes' used to prove
cohomological finite generation is equivalent to some recent `untwisting
theorems' in the theory of strict polynomial functors. We actually provide
thereby a new proof of these theorems.
