Physical systems characterized by long range interactions  are ubiquitous, encompassing systems as diverse as self-gravitating bodies in astrophysics, plasmas, lasers, cold atoms  in the laboratory, and even biological systems. One of the main results of recent years about such systems is that, quite generically, they relax, on times scales characterized by the mean force field, towards long-lived macroscopic states called quasi-stationary states (QSS) [e.g. galaxies in astrophysics, the red spot of Jupiter, steady states of free electron laser]. These out-of-equilibrium states have a typical life-time diverging with particle number, while on shorter time scales they are described within the framework of the Vlasov equation. These results apply to strictly conservative systems in a microcanonical framework, and the question inevitably arises of the robustness of such states beyond this idealized limit.