A successful statistical description of most nonlinear systems is stymied by the lack of closure; the rates of change of lower order moments depend on moments of higher order leading to an infinite hierarchy. Most attempts to enforce an artificial closure fail. However, there is a natural asymptotic closure for fields of weakly nonlinear waves (think of a wind driven ocean surface). I will explain to you what (mild) premises are required to achieve this natural closure and the reasons it occurs. The corresponding kinetic equation for the energy density turns out to have very interesting stationary solutions corresponding to equipartition states and to finite flux solutions of Kolmogorov type, discovered originally by our good colleague Volodja Zakharov. But, despite many successes, the story is far from over as there are still open challenges, some of which I will tell you about.