This note is an overview of the Poisson sigma model (PSM) and
its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance as branes of the PSM, quantization in terms of L1- and A1-algebras, and bimodule structures are recalled. As an application, an “almost” functorial quantization of Poisson maps is presented if no anomalies occur. This leads in principle to a novel approach for the quantization of Poisson–Lie groups.