In this talk I'm going to present a series of recent results about the long time complex dynamics of the water waves equations for a bi-dimensional fluid under the action of gravity and eventually capillary forces, with space periodic boundary conditions. This is an infinite dimensional Hamiltonian system with a quasi-linear nonlinearity. We shall discuss both long time existence results based on Birkhoff normal form arguments as well as bifurcation of small amplitude time quasi-periodic solutions (which are in particular global in time).