Linear response theory aims at predicting the mean properties of a dynamical system subject to external perturbations. It is first order approximation that relates the natural variability of the system with its ability to mitigate small disturbances. To this end, the eigenvalues of the Fokker-Planck operator associated with the unperturbed system provide the asymptotic rates at which the system attains a new and, possibly, non-equilibrium steady-state. When such operators, however, are non-selfadjoint, the dynamics become more sensitive, and the relaxation rates do not explain the transient behavior of the system. In this talk, we discuss the role of non-selfadjointness in deriving fluctuation-response relations for stochastic and chaotic systems.