Abstract. 
In this talk, I will first review the main features of the Kuramoto model
(in its continuum limit), and previous attempts to prove them rigorously. 
Then, I will present our recent results on the asymptotic stability of 
basic - either incoherent or partially locked - stationary states, that provide 
a portray of the phenomenology in broad range of parameters.
Joint works with D. Gérard-Varet and G. Giacomin