Let G be a reductive Lie group. The Langlands classification describes the set \Pi_a(G) of irreducible admissible G-representations in terms of conjugacy classes in the Langlands dual group. Inside \Pi_a(G) is the subset \Pi_u(G) of irreducible *unitary* G-representations. It is natural to ask: what does the Langlands classification tell us about \Pi_u(G)? In this talk, I will review an approach to this problem originating in the work of Arthur and describe some recent progress towards its solution.