  We consider the series of the Bergman orthogonal polynomials associated with
a bounded simply-connected domain in the complex plane, whose boundary is a
Jordan curve. These are the polynomials that are orthonormal with respect to
the area measure on the domain. The purpose of this note is to report on recent
results regarding the fine asymptotic behaviour of the the leading coefficients
and the polynomials in the complement of the domain, in cases when the boundary
includes corners. These results complement an investigation started in the
1920's by T. Carleman, who obtained the fine asymptotics for domains with
analytic boundaries and carried over by P.K. Suetin in the 1960's, who
established them for domains with smooth boundaries.
