### Abstract

The classical second-order non-linear Painleve equations appear in many scientific applications as mathematical models. Their roles as models demand asymptotic information about their highly transcendental solutions. We will introduce methods to (i) find asymptotic behaviours of the solutions in various limits; (ii) show how to extend such techniques to gain global information; (iii) find error estimates; (iv) extend these methods to higher-order Painleve equations; and (v) if time permits, discuss asymptotics of discrete Painleve equations.