Although several results on complete integrability of infinite dimensional Hamiltonian systems have been established, none of them provides a description of the phase space as paradigmatic as the one given by the Arnold-Liouville theorem in finite dimension. This is largely due to the topology of the phase space. In this talk, I shall discuss this theorem in infinite dimension and try to give a more geometric understanding of integrability in this frame, in terms of foliations in infinite tori and construction of Action-Angle variables in an open set of the phase space. This is part of a joint work with L. Baroni and M. Procesi.