  Recently, QCD Dirac spectra have been obtained for reasonably large lattices.
We argue that correlations of these spectra are universal and can be obtained
from a random matrix model with the global symmetries of QCD. Analytical
arguments are presented to support this claim. Detailed comparisons with
lattice results are made. We analyze spectral correlations in the bulk of the
spectrum and find that long range fluctuations are strongly suppressed in
complete agreement with random matrix theory. We study the valence quark mass
dependence of the lattice QCD Dirac operator showing that the average spectral
density near zero virtuality is given by chiral random matrix theory. This
agrees with recent lattice calculations of the microscopic spectral density. of
this lecture, we introduce a schematic random matrix model for the chiral phase
transition at nonzero chemical potential. We consider both real, complex and
quaternion real matrix elements. We find a remarkable triality for the
distribution of of the eigenvalues in the complex plane. In particular, this
elucidates the nature of the quenched approximation in each case.
