  An overview is given of recent advances in the nonequilibrium statistical
mechanics of quantum systems and, especially, of time-reversal symmetry
relations that have been discovered in this context. The systems considered are
driven out of equilibrium by time-dependent forces or by coupling to large
reservoirs of particles and energy. The symmetry relations are established for
the exchange of energy and particles between the subsystem and its environment.
These results have important consequences. In particular, generalizations of
the Kubo formula and the Casimir-Onsager reciprocity relations can be deduced
beyond linear response properties. Applications to electron quantum transport
in mesoscopic semiconducting circuits are discussed.
