This paper summarizes recent results how to obtain approximate one-electron potentials describing exchange and correlation which depend on the local electron density. Following the lines given by Hohenberg, Kohn and Sham explicit results are given in two versions of the theory ; one to describe ground state properties and one for excitation energies. The extension to spin polarized systems is discussed and some new results are presented. The paper also summarizes recent results about the linear response properties and comments on the role of the non-locality of the self-energy