Nonlinear Liouville equations are self consistent 1-degree of freedom (or d-degrees of freedom) Hamiltonian systems, like Vlasov Poisson Equation (VPE); 2D Euler ; and the Hamiltonian mean field model (HMF). Understanding the long time behavior of these equations is a long standing challenging problem. I'll make a short review of known rigorous results about asymptotic behavior of solutions of Vlasov-like equations: stationary stable solutions, BGK waves for VPE and rotating solutions for 2D Euler; Landau Damping and rinviscid damping, and I will remind and comment some results form statistical mechanics approaches to the problem. Finally I'll discuss the possibility of building Eulerian periodic, and Langrangian chaotic, solutions for Vlasov like equations in the spirit of Morita and Kaneco 2006.