The wave turbulence theory provides a unified nonequilibrium thermodynamic formulation of random nonlinear optical waves. The talk will review different formalisms: the wave turbulence kinetic equation describing wave condensation and thermalization, as well as a breakdown of thermalization in analogy with the Fermi-Pasta-Ulam problem, the long-range Vlasov equation in analogy with Gravitation, the weak Langmuir turbulence kinetic equation and its description of spectral incoherent solitons and incoherent dispersive shocks through a family of singular integro-differential kinetic equations. Extreme events appear under different forms within these different formalisms.