I will present a joint work with A. Ionescu proving that smooth solutions to the energy critical nonlinear Schrodinger equation on T3 remain global in time. One interest of this is that it clarifies the possible obstructions to global existence of the energy critical equation on manifolds due to trapped geodesics and finite volume. This relies on previous work by Bourgain, Colliander-Keel-Staffilani-Takaoka-Tao and Herr-Tataru-Tzvetkov.