  Fidelity serves as a benchmark for the relieability in quantum information
processes, and has recently atracted much interest as a measure of the
susceptibility of dynamics to perturbations. A rich variety of regimes for
fidelity decay have emerged. The purpose of the present review is to describe
these regimes, to give the theory that supports them, and to show some
important applications and experiments. While we mention several approaches we
use time correlation functions as a backbone for the discussion. Vanicek's
uniform approach to semiclassics and random matrix theory provides an important
alternative or complementary aspects. Other methods will be mentioned as we go
along. Recent experiments in micro-wave cavities and in elastodynamic systems
as well as suggestions for experiments in quantum optics shall be discussed.
