Ginzburg, Kazhdan and Lusztig's proof of the Deligne-Langlands conjecture established a bijection between irreducible representations of the affine Hecke algebra and certain Langlands parameters involving q-commuting nilpotent-semisimple elements. We will describe a categorification of this bijection, namely, an equivalence of categories between the derived category of modules for the affine Hecke algebra and the Springer block of the category of "unipotent affine character sheaves." The proof involves ideas from Hochschild homology, derived algebraic geometry, and derived Theta stratifications. This is a joint work with David Ben-Zvi, David Helm and David Nadler.