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

Equilibrium and out of equilibrium phase transitions in systems with long range interactions and in 2D flows