  In 1972 H. L. Montgomery announced a remarkable connection between the
distribution of the zeros of the Riemann zeta-function and the distribution of
eigenvalues of large random Hermitian matrices. Since then a number of
startling developments have occurred making this connection more profound. In
particular, random matrix theory has been found to be an extremely useful
predictive tool in the theory of L-functions. In this article we will try to
explain these recent developments and indicate some diretions for future
investigations.
