The Poisson sigma model is a topological field theory with target a Poisson manifold. Its perturbative expansion in local coordinates yields Kontsevich's formula. The model is however anomalous under target diffeomorphisms and this is responsible, in particular, for the complications in defining a global star product, which however can be defined. How this is refelected in the path integral formalism will be addressed (as far as the speaker understands it) in the last part of the talk.