Bergman, Szegő, Faber and Christoffel: boundary behavior

Let $G$ be a bounded simply-connected domain in the complex plane $\mathbb{C}$, with Jordan boundary $\Gamma$. We review some recent and present some new results on the asymptotic boundary behaviour of Bergman, Szegő and Faber polynomials, under various assumptions on the properties of $\Gamma$. These will lead to some new estimates for the asymptotic behaviour on $\Gamma$ of the associated Christoffel functions.