The self-consistent theory of Anderson localization of quantum particles or
classical waves in disordered media is reviewed. After presenting the basic
concepts of the theory of Anderson localization in the case of electrons in
disordered solids, the regimes of weak and strong localization are discussed.
Then the scaling theory of the Anderson localization transition is reviewed.
The renormalization group theory is introduced and results and consequences are
presented. It is shown how scale-dependent terms in the renormalized
perturbation theory of the inverse diffusion coefficient lead in a natural way
to a self-consistent equation for the diffusion coefficient. The latter
accounts quantitatively for the static and dynamic transport properties except
for a region near the critical point. Several recent applications and
extensions of the self-consistent theory, in particular for classical waves,
are discussed.Comment: 25 pages, 2 figures; published version including correction