  This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics
in random matrix models and its applications. We discuss the following topics:
random matrix models and orthogonal polynomials, the Riemann-Hilbert approach
to the large $N$ asymptotics of orthogonal polynomials and its applications to
the problem of universality in random matrix models, the double scaling limits,
the large $N$ asymptotics of the partition function, and random matrix models
with external source.
