  In this chapter of the Oxford Handbook of Random Matrix Theory we introduce
chiral Random Matrix Theories with the global symmetries of QCD. In the
microscopic domain, these theories reproduce the mass and chemical potential
dependence of QCD. The main focus of this chapter is on the spectral properties
of the QCD Dirac operator and relations between chiral Random Matrix Theories
and chiral Lagrangians. Both spectra of the anti-hermitian Dirac operator and
spectra of the nonhermitian Dirac operator at nonzero chemical potential are
discussed.
