The macroscopic fluctuation theory, proposed in collaboration with L. Bertini. A. De
Sole, D. Gabrielli and C. Landim to study diffusive systems out of equilibrium, developed
over the last decade into a powerful tool to solve concrete problems. After discussing
the basic ideas I will illustrate some applications among which the existence of phase
transitions in the behaviour of fluctuations. Of special interest are the fluctuations
of the current in stationary states. New variational principles appear in the
thermodynamics of non-equilibrium stationary states.