Crossed modules and Galois cohomology of reductive groups The main aim of this talk is to report on M. Borovoi's work in the early nineties on `abelian Galois cohomology' of reductive groups, and the way it uses crossed modules. I will also say something on my current work in progress with Borovoi, which clarifies the link between the abelian Galois cohomology of reductive groups and more geometric invariants, such as the Brauer group.