These lecture
give a short review of methods such as the matrix ansatz, the
additivity principle or the macroscopic fluctuation theory, developed recently
in the theory of non-equilibrium phenomena. They show how these methods
allow to calculate the fluctuations and large deviations of the
density and of the current in non-equilibrium steady states of systems
like exclusion processes. The properties of
these fluctuations and large deviation functions in non-equilibrium
steady states (for example non-Gaussian fluctuations of density or
non-convexity of the large deviation function which generalizes the notion of free
energy) are compared with those of
systems at equilibrium.