Asymptotics of orthogonal polynomials and the Painlev\'e transcendents

In this survey, we review asymptotic results of some orthogonal polynomials which are relate to the Painlev'e transcendents. They are obtained by applying Deift-Zhou’s nonlinear steepest descent method for Riemann-Hilbert problems. In the last part of this article, we list several open problems.