The Isomorphism Conjectures due to Farrell-Jones and Baum-Connes predict a description of the algebraic $K$-theory of group rings and the topological $K$-theory of reduced group $C^*$-algebras, in terms of algebraic topology. A theorem of Higson and Kasparov establishes the Baum-Connes conjecture for Haagerup groups. In joint work with G. Cortiñas we have shown how to adapt their techniques to prove the Farrell-Jones conjecture for Haagerup groups with coefficents in stable $C^*$-algebras.