  Two fundamental ingredients play a decisive role in the foundation of
fluctuation relations: the principle of microreversibility and the fact that
thermal equilibrium is described by the Gibbs canonical ensemble. Building on
these two pillars we guide the reader through a self-contained exposition of
the theory and applications of quantum fluctuation relations. These are exact
results that constitute the fulcrum of the recent development of nonequilibrium
thermodynamics beyond the linear response regime. The material is organized in
a way that emphasizes the historical connection between quantum fluctuation
relations and (non)-linear response theory. We also attempt to clarify a number
of fundamental issues which were not completely settled in the prior
literature. The main focus is on (i) work fluctuation relations for transiently
driven closed or open quantum systems, and (ii) on fluctuation relations for
heat and matter exchange in quantum transport settings. Recently performed and
proposed experimental applications are presented and discussed.
