Asymptotic affine Hecke algebras were defined by Lusztig in 1987 using Kazhdan-Lusztig bases of affine Hecke algebras. It turns out that the Asymptotic affine Hecke algebras are interesting in understanding representations of affine Hecke algebras and have nice relations with equivariant K-theory. The main subject of this talk is Lusztig’s conjecture on the structure of asymptotic affine Hecke algebras which establishes a relation between asymptotic affine Hecke algebras and certain equivariant K-groups.