We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also m
ake connections to the unified transform method due to A.S. Fokas and co-authors, analysing particular instances of this method, proposed by J.A. DeSanto and co-authors, for problems of acoustic scattering by diffraction gratings.
