This talk aims to give a gentle exposition of recent work establishing an algebraic structure on the groups H^k(GL_nZ; Q). These cohomology groups are of interest in several areas of mathematics, and computing them has proven extremely difficult. One approach to studying these groups is via "Steinberg modules", which are defined in terms of certain simplicial complexes. After giving a brief introduction to these objects, I will describe a combinatorial way to put a product and coproduct structure on the Steinberg modules, and discuss recent work of Ash-Miller-Patzt that used this to deduce a Hopf algebra structure on the cohomology H^k(GL_nZ; Q), and describe how this helps in finding new cohomology classes.