  We review the application of random matrix theory (RMT) to chiral symmetry in
QCD. Starting from the general philosophy of RMT we introduce a chiral random
matrix model with the global symmetries of QCD. Exact results are obtained for
universal properties of the Dirac spectrum: i) finite volume corrections to
valence quark mass dependence of the chiral condensate, and ii) microscopic
fluctuations of Dirac spectra. Comparisons with lattice QCD simulations are
made. Most notably, the variance of the number of levels in an interval
containing $n$ levels on average is suppressed by a factor $(\log n)/\pi^2 n$.
An extension of the random matrix model model to nonzero temperatures and
chemical potential provides us with a schematic model of the chiral phase
transition. In particular, this elucidates the nature of the quenched
approximation at nonzero chemical potential.
