A 2-group (or a crossed-module) is a categorified version of a group. Line bundles over a scheme, for instance, form the Picard 2-group. Galois cohomology of 2-groups can be used to give information about Galois cohomology of ordinary groups (via, say, certain long exact sequences). I will discuss the basics of the theory and give some simple examples involving Picard and Brauer groups. Time permitting, I will explain Borovoi’s application of these ideas to the study of Galois cohomology of reductive groups.