  We review generalized Fluctuation-Dissipation Relations which are valid under
general conditions even in ``non-standard systems'', e.g. out of equilibrium
and/or without a Hamiltonian structure. The response functions can be expressed
in terms of suitable correlation functions computed in the unperperturbed
dynamics. In these relations, typically one has nontrivial contributions due to
the form of the stationary probability distribution; such terms take into
account the interaction among the relevant degrees of freedom in the system. We
illustrate the general formalism with some examples in non-standard cases,
including driven granular media, systems with a multiscale structure, active
matter and systems showing anomalous diffusion.
