Luc Rey-Bellet Statistical mechanics of anharmonic lattices (247K, Postscript) ABSTRACT. This paper is a review on the statistical mechanics of anharmonic oscillators coupled to heat reservoirs. We discuss stationary states (existence and ergodic properties) and entropy production (positivity, Green-Kubo formulas and the Gallavotti-Cohen fluctuation theorem). This review will appear in the Proceedings of the 2002 UAB International Conference on Differential Equations and Mathematical Physics.