Different Poisson structures have been proposed to give a Hamiltonian formulation to evolution equations issued from fluid mechanics. In this talk, I will investigate the main brackets which appear in the literature and discuss the difficulties which arise when one tries to give a rigorous meaning to these brackets. In the first part of my talk, I will recall basic material on Poisson brackets on a finite dimensional manifold and present the difficulties which arise when one extend these concepts to infinite dimensional manifolds. In the second part of my talk, I will focus on the problem of defining a valid and usable bracket to study rotational fluid flows with a free boundary. I will discuss some results which have emerged in the literature to solve the difficulties which arise and conclude that (up to my knowledge) the main problems are still open.