KAM and Normal form theory have proved to be a very powerful tool in the study of finite dimensional dynamical systems. From a conceptual point of view, the reason is that KAM theory allows to construct almost all solutions of a close to integrable system. From an applicative point of view, the corresponding mathematical tools, essentially normal form theory, are by now usually employed to speed by orders of magnitude computations of physical systems and in particular to plan space flights. This is the long time perspective of the development of KAM and normal form theory for PDEs, which should allow to understand general ``regular'' solutions of Hamiltonian PDEs and also provide new powerful tools for the computation of the dynamics of systems ranging from fluid dynamics to quantum mechanics and plasma physics. Part of the problem, largely still open, is to understand and define what is the “typical” dynamical behavior of the flow of a PDE.