  This paper reviews the recent mathematical progresses made on the study of
the orbital stability properties for the gravitational Vlasov-Poisson system.
We present in details the paper of Lemou, M\'ehats and Rapha\"el (Inventiones
2011) and we review also the previous works by Dolbeault, Guo, Hadzic, Lin,
Rein, S\'anchez, Soler, Wan, Wolansky. We also include a discussion of the
history of this topic and the pioneering works by physicists like Antonov,
Lynden-Bell and Aly. This is the text of a Bourbaki seminar given in november
2011
