The purpose of the talk is to explain joint work with Nikolaus and Schlichting in which we obtain formulas for the L-groups of real C*-algebras in terms of their topological K-groups. The main tool to do this is to first obtain a formula for the L-spectrum in terms of the topological K-spectrum and derive the results about groups from this spectrum level result. In the first part of the talk, I will give an introduction to algebraic L-theory and explain a homotopy theoretic characterisation of KK theory which will be used crucially in our proof. In the second part of the talk, I will then indicate how to this homotopy theoretic KK-theory to obtain the spectrum level comparison between K- and L-theory and how one can derive the group-level comparison.