In this work we provide efficient numerical methods for the numerical solution of Partial Differential Equations (PDEs) and the computation of the associated outputs of interest, also in the frame of optimal control problems. With this aim, a goal-oriented analysis could be conveniently adopted in order to estimate the errors associated with the computation of such output functionals by means of Galerkin methods, remarkably the Finite Elements (FE) and Reduced Basis (RB) ones. Anisotropic mesh adaption procedures, driven by a posteriori error estimators, are used in the context of the FE method in order to capture the directional features of the solution, while the RB method is considered for the solution of parametrized PDEs and parametrized optimal control problems. In particular, we focus on environmental applications, specifically on atmosphere ic pollution problems, even if the methods considered can be conveniently used for a broad range of Engineering applications.