Alan Newell University of Arizona Wave turbulence is the study of the long time statistical behavior of a sea of weakly nonlinear dispersive waves, solutions of weakly nonlinear field equations,in the presence of sources and sinks. Because it has an asymptotic closure and all cumulant behaviors can be calculated from the waveaction density which satisfies a closed, integral differential equation, called the kinetic equation, the problem is generally assumed to be solved. While it is true that there have been successes and that analytically derived behaviors shed light on turbulence in general, there are still many open questions. The purpose of the lecture will be to outline the theory, point to the weaknesses, in some cases show how to address those flaws, and introduce new challenges.