Turbulence is a general term used for describing the erratic motions displayed by nonlinear systems that are driven far from their equilibrium position and thus display complicated motions involving different time and length scales. Wave turbulence (WT) share many common ideas with turbulence, in particular as being a statistical theory for out-of-equilibrium systems. A main difference resides in the fact that the persistence of waves is assumed. The application of WT to vibrating plates started with the theoretical derivation of the kinetic equation from the dynamical von Karman equations that describe large-amplitude motions of thin plates. Since this date, numerous papers have been published covering experimental, theoretical and numerical materials. In fact, it appears that the vibrating plate is a perfect candidate for a thorough comparison of experiments with theoretical predictions. As compared to other physical systems such as capillary or gravity waves for example, an experimental set-up with a fine control of energy injection and a confortable range of wavelength is not too difficult to put in place. Secondly, the available measurement techniques allow one to get a complete and precise picture of the dynamics through the scales, both in the space and frequency domains. Finally, numerical codes with good accuracy have been developed so that all the underlying assumptions of the theory as well as its predictions have been tested, both on the experimental and the numerical levels.