  In this lecture we review recent lattice QCD studies of the statistical
properties of the eigenvalues of the QCD Dirac operator. We find that the
fluctuations of the smallest Dirac eigenvalues are described by chiral Random
Matrix Theories with the global symmetries of the QCD partition function.
Deviations from chiral Random Matrix Theory beyond the Thouless energy can be
understood analytically by means of partially quenched chiral perturbation
theory.
