A control system is an evolution equation depending on some parameter. Control theory aims at determining how one can suitably choose this parameter as a function of time in order to modify the dynamics of the system in a prescribed way. In particular, the controllability problem raises the question whether it is possible to steer the state of the system from any initial state to any prescribed target. The problem of asymptotic stabilization wonders whether it is possible to make an equilibrium point stable. When it comes to nonlinear systems, the usual approach consists in linearizing the system and in proving a result on the linear system by using classical techniques. However in many physical situations, the linearized system fails to be controllable. The return
method has been introduced by J.-M. Coron in order to circumvent this difficulty. To illustrate this method, we will first consider the problem for which this method has been introduced. It concerns the asymptotic stabilization of finite dimensional control systems. Then we will illustrate the method with two examples coming from fluid mechanics. The first example, due to J.-M. Coron, concerns the Euler equation for perfect incompressible fluids. The second example, due to J.-M. Coron and S. Guerrero, concerns the Navier-Stokes equation.