We consider the stochastic Burgers equation from a Lagrangian viewpoint. In other words, we study the dynamical behaviour of the energy minimisers which give the variational behaviour of the solution. Under non-degeneracy assumptions on the random forcing, we prove hyperbolicity of these minimisers, considerably simplifying the proof in [E, Khanin, Mazel, Sinai, Annals, 2000]. Finally, we will speak about the relationship between this problem and the convergence to the stationary measure for the solutions of the equations. This is a joint work with K. Khanin (Toronto).