Appears in collection : Mathematical aspects of the physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints

It has been an empirical fact since the 60s that a perturbed black hole returns to its ground state by producing radiation at a discrete set of complex frequencies. While this strongly suggests the spectrum of some non-self-adjoint operator underlies this phenomenon, a clean understanding of how this comes about has only been established fairly recently. I will review results obtained so far and discuss open directions.