Current fluctuations in non-equilibrium systems

This talk will review a series of results obtained recently on the fluctuations of current in diffusive systems for several geometries: steady state obtained by contact with two reservoirs or two heat baths, system at equilibrium on a ring geometry, two systems at unequal temperatures which are connected at time t=0. Some open questions will also be discussed, in particular the behavior of one dimensional mechanical systems and its similarity with diffusive systems at a phase transition.