  This review paper is devoted to a presentation of recent progress in wave
turbulence. I first present the context and state of the art of this field of
research both experimentally and theoretically. I then focus on the case of
wave turbulence on the surface of a fluid, and I discuss the main results
obtained by our group: caracterization of the gravity and capillary wave
turbulence regimes, the first observation of intermittency in wave turbulence,
the occurrence of strong fluctuations of injected power in the fluid, the
observation of a pure capillary wave turbulence in low gravity environment and
the observation of magnetic wave turbulence on the surface of a ferrofluid.
Finally, open questions in wave turbulence are discussed.
