It is well known that the phase space of a finite dimensional integrable system is filled by invariant tori; KAM theory ensures that most of them persist under small perturbation. In PDEs the situation is much more complicated, and the only quite complete theory that we know, allows to deal with Hamiltonian PDEs in one space dimension and only allows to show persistence of finite dimensional tori. A few eamples in higher dimensions are also known. Also some preliminary results on the persistence of infinite dimensional tori are known. In this talk I will present some of the above results and discuss some open problems related to the possible application to Gross Pitaevskii equation.