  In self-gravitating stars, two dimensional or geophysical flows and in
plasmas, long range interactions imply a lack of additivity for the energy; as
a consequence, the usual thermodynamic limit is not appropriate. However, by
contrast with many claims, the equilibrium statistical mechanics of such
systems is a well understood subject. In this proceeding, we explain briefly
the classical approach to equilibrium and non equilibrium statistical mechanics
for these systems, starting from first principles. We emphasize recent and new
results, mainly a classification of equilibrium phase transitions, new
unobserved equilibrium phase transition, and out of equilibrium phase
transitions. We briefly discuss what we consider as challenges in this field.
