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We review recent progress in our theoretical understanding of stronglycorrelated fermion systems in the presence of disorder. Results were obtainedby the application of a powerful nonperturbative approach, the DynamicalMean-Field Theory (DMFT), to interacting disordered lattice fermions. Inparticular, we demonstrate that DMFT combined with geometric averaging overdisorder can capture Anderson localization and Mott insulating phases on thelevel of one-particle correlation functions. Results are presented for theground-state phase diagram of the Anderson-Hubbard model at half filling, bothin the paramagnetic phase and in the presence of antiferromagnetic order. Wefind a new antiferromagnetic metal which is stabilized by disorder. Possiblerealizations of these quantum phases with ultracold fermions in opticallattices are discussed.

Anderson localization vs. Mott-Hubbard metal-insulator transition in disordered, interacting lattice fermion systems