  Zonal jets are striking and beautiful examples of the propensity for
geophysical turbulent flows to spontaneously self-organize into robust, large
scale coherent structures. There exist many dynamical mechanisms for the
formation of zonal jets: statistical theories (kinetic approaches, second order
or larger oder closures), deterministic approaches (modulational instability,
$\beta$-plumes, radiating instability, zonostrophic turbulence, and so on). A
striking remark is that all these different dynamical approaches, each of them
possibly relevant in some specific regimes, lead to the same kind of final jet
structures. Is it then possible to have a more general explanation of why all
these different dynamical regimes, from fully turbulent flows to gentle
quasilinear regime, consistently lead to the same jet attractors ? Equilibrium
statistical mechanics provides an answer to this general question. Here we we
present the salient features of this theory and review applications of this
approach to the description of zonal jets. We show that equilibrium states on a
beta plane or a sphere are usually zonal or quasi-zonal, and that increasing
the energy leads to bifurcations breaking the zonal symmetry.
