  We review briefly the concepts underlying complex systems and probability
distributions. The later are often taken as the first quantitative
characteristics of complex systems, allowing one to detect the possible
occurrence of regularities providing a step toward defining a classification of
the different levels of organization (the ``universality classes''). A rapid
survey covers the Gaussian law, the power law and the stretched exponential
distributions. The fascination for power laws is then explained, starting from
the statistical physics approach to critical phenomena, out-of-equilibrium
phase transitions, self-organized criticality, and ending with a large but not
exhaustive list of mechanisms leading to power law distributions. A check-list
for testing and qualifying a power law distribution from your data is described
in 7 steps. This essay enlarges the description of distributions by proposing
that ``kings'', i.e., events even beyond the extrapolation of the power law
tail, may reveal an information which is complementary and perhaps sometimes
even more important than the power law distribution. We conclude a list of
future directions.
