In this survey we give a brief introduction to orthogonal polynomials,including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials,and the Deift & Zhou method of steepest descent. We illustrate this new approach,and a modified version,with the Hermite polynomials. Other recent progress of this method is also mentioned,including applications to discrete orthogonal polynomials,orthogonal polynomials on curves,multiple orthogonal polynomials,and certain orthogonal polynomials with singular behavior.
