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We present a self-consistent theory of Anderson localization that yields asimple algorithm to obtain \emph{typical local density of states} as an orderparameter, thereby reproducing the essential features of a phase-diagram oflocalization-delocalization quantum phase transition in the standard latticemodels of disordered electron problem. Due to the local character of ourtheory, it can easily be combined with dynamical mean-field approaches tostrongly correlated electrons, thus opening an attractive avenue for a genuine{\em non-perturbative} treatment of the interplay of strong interactions andstrong disorder.Comment: 7 pages, 4 EPS figures, revised version to appear in Europhysics  Letter

Typical medium theory of Anderson localization: A local order parameter approach to strong-disorder effects