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..