  We study the probability distribution of a current flowing through a
diffusive system connected to a pair of reservoirs at its two ends. Sufficient
conditions for the occurrence of a host of possible phase transitions both in
and out of equilibrium are derived. These transitions manifest themselves as
singularities in the large deviation function, resulting in enhanced current
fluctuations. Microscopic models which implement each of the scenarios are
presented, with possible experimental realizations. Depending on the model, the
singularity is associated either with a particle-hole symmetry breaking, which
leads to a continuous transition, or in the absence of the symmetry with a
first-order phase transition. An exact Landau theory which captures the
different singular behaviors is derived.
