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The Random Matrix Model approach to Quantum Chromodynamics (QCD) withnon-vanishing chemical potential is reviewed. The general concept using globalsymmetries is introduced, as well as its relation to field theory, theso-called epsilon regime of chiral Perturbation Theory (echPT). Two types ofMatrix Model results are distinguished: phenomenological applications leadingto phase diagrams, and an exact limit of the QCD Dirac operator spectrummatching with echPT. All known analytic results for the spectrum of complex andsymplectic Matrix Models with chemical potential are summarised for thesymmetry classes of ordinary and adjoint QCD, respectively. These includecorrelation functions of Dirac operator eigenvalues in the complex plane forreal chemical potential, and in the real plane for imaginary isospin chemicalpotential. Comparisons of these predictions to recent Lattice simulations arealso discussed.Comment: 40 pages, invited review for Int.J.Mod.Phys.

MATRIX MODELS AND QCD WITH CHEMICAL POTENTIAL