  There is no compelling reason imposing that the methods of statistical
mechanics should be restricted to the dynamical systems which follow the usual
Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and
artificial systems exhibit complex dynamics, for instance, generic stationary
states which are {\it not} ergodic nor close to it, in any geometrically simple
subset of the {\it a priori} allowed phase space, in any (even extended)
trivial sense. A vast class of such systems appears, nevertheless, to be
tractable within thermostatistical methods completely analogous to the usual
ones. The question posed in the title arises then naturally. Some answer to
this complex question is advanced in the present review of nonextensive
statistical mechanics and its recent connections.
