The Kohn-Sham model is a powerful,widely used approach for computation of ground state electronic energies and densities in chemistry,materials science,biology,and nanoscience.In this presentation,we will talk about our study for adaptive finite element approximations for the Kohn-Sham model.Based on the residual type a posteriori error estimators,we introduce an adaptive finite element algorithm,and obtain both the asymptotic contraction property and asymptotic quasi-optimal complexity of the adaptive finite element approximations.