  In this review we first outline the basics of transport theory and its recent
generalization to off-shell transport. We then present in some detail the main
ingredients of any transport method using in particular the Giessen
Boltzmann-Uehling-Uhlenbeck (GiBUU) implementation of this theory as an
example. We discuss the potentials used, the ground state initialization and
the collision term, including the in-medium modifications of the latter. The
central part of this review covers applications of GiBUU to a wide class of
reactions, starting from pion-induced reactions over proton and antiproton
reactions on nuclei to heavy-ion collisions (up to about 30 AGeV). A major part
concerns also the description of photon-, electron- and neutrino-induced
reactions (in the energy range from a few 100 MeV to a few 100 GeV). For this
wide class of reactions GiBUU gives an excellent description with the same
physics input and the same code being used. We argue that GiBUU is an
indispensable tool for any investigation of nuclear reactions in which
final-state interactions play a role. Studies of pion-nucleus interactions,
nuclear fragmentation, heavy ion reactions, hyper nucleus formation,
hadronization, color transparency, electron-nucleus collisions and
neutrino-nucleus interactions are all possible applications of GiBUU and are
discussed in this article.
