  In this paper we review some general properties of probability distributions
which exibit a singular behavior. After introducing the matter with several
examples based on various models of statistical mechanics, we discuss, with the
help of such paradigms, the underlying mathematical mechanism producing the
singularity and other topics such as the condensation of fluctuations, the
relationships with ordinary phase-transitions, the giant response associated to
anomalous fluctuations, and the interplay with Fluctuation Relations.
