This article is an introduction to the monograph [ECR], the purpose of which was to classify the automorphic representations of a family of classical groups. The groups are quasisplit, special orthogonal and symplectic groups G. Their representations are classified in terms of those of general linear groups GLpNq. The monograph is based on the stabilization of the trace formula for G, established for any connected group in [A1]. It also depends on the stabilization of the twisted trace formula for GLpNq, which represents work in progress by Moeglin and Waldspurger [W5]–[W7], [MW2]. Until it has been completed, the classification will remain conditional. There are already two short surveys [A4], [A5] of some of the main results of [ECR]. This article is somewhat different. I have tried to write it as a longer report that might be suitable for the broader readership of Current Developments in Mathematics. The monograph [ECR] is long, and