In this talk I will discuss some recent work related to torsion in the cohomology of arithmetic groups, and its connection to the Langlands program. I will focus primarily on stability phenomena in the cohomology of SL_n (joint work of the speaker with Frank Calegari). I will also discuss some other examples involving cohomology in low degree (joint work of the speaker with Toby Gee), as well as other recent work on this topic (Calegari--Venkatesh, Scholze) . As I hope to explain, these examples suggest that the deep harmonic analytic theory of automorphic forms, due to Langlands, Arthur, etc., should have an analogue in the torsion world, the precise nature of which remains to be understood.