In this paper we consider the first exit problem of an overdamped Lévy driven particle in a confining potential. We survey results obtained in recent years from our work on the Kramers’ times for dynamical systems of this type with Lévy perturbations containing heavy, and exponentially light jumps, and compare them to the well known case of dynamical systems with Gaussian perturbations. It turns out that exits induced by Lévy processes with jumps are always essentially faster than Gaussian exits
