  In this review, we scrutinize historical and modern results on the linear
response of dynamic systems to external perturbations and the celebrated
relationship between fluctuations and dissipation expressed by the
Fluctuation-Dissipation Theorem (FDT). The conceptual derivation of FDT
originated from the definition of the equilibrium state and Onsager's
regression hypothesis. Over the time the fluctuation-dissipation relation was
vividly investigated also for systems away from equilibrium, frequently
exhibiting wild fluctuations of measured parameters. In the review, we recall
the major formulations of the FDT, such as those proposed by Langevin, Onsager
and Kubo. We discuss as well the importance of fluctuations in a wide class of
growth phenomena. We point out possible generalizations of the FDT formalism
along with a discussion of situations where the relation breaks down and can be
not adapted.

Statistical Mechanics