In this chapter, the aim is the solving of variational inclusions fo the form 0_in f(x)+F(x), where f is a subanalytic and locally Lipschitz function, F is a set-valued map with closed graph. The methods are developped using the metric regularity of (f+F) or the Aubin property of (f+F)^{-1}, and often lead to a superlinear convergence.