  A variety of phenomena in nuclear and high energy physics seemingly do not
satisfy the basic hypothesis for possible stationary states to be of the type
covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the
system appears to relax, along time, on macroscopic states which violate the
ergodic assumption. Some of these phenomena appear to follow, instead, the
prescriptions of nonextensive statistical mechanics. In the same manner that
the BG formalism is based on the entropy $S_{BG}=-k \sum_i p_i \ln p_i$, the
nonextensive one is based on the form $S_q=k(1-\sum_ip_i^q)/(q-1)$ (with
$S_1=S_{BG}$). Typically, the systems following the rules derived from the
former exhibit an {\it exponential} relaxation with time toward a stationary
state characterized by an {\it exponential} dependence on the energy ({\it
thermal equilibrium}), whereas those following the rules derived from the
latter are characterized by (asymptotic) {\it power-laws} (both the typical
time dependences, and the energy distribution at the stationary state). A brief
review of this theory is given here, as well as of some of its applications,
such as electron-positron annihilation producing hadronic jets, collisions
involving heavy nuclei, the solar neutrino problem, anomalous diffusion of a
quark in a quark-gluon plasma, and flux of cosmic rays on Earth. In addition to
these points, very recent developments generalizing nonextensive statistical
mechanics itself are mentioned.
