Equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model

This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov-Poisson model to the astrophysical systems like globular clusters or galaxies. In a second part we will recall some recent numerical results which may give us some some quantitative hints about the equilibrium state associated to those systems.