  Exoplanets are often found with short periods or high eccentricities, and
multiple-planet systems are often in resonance. They require dynamical theories
that describe more extreme motions than those of the relatively placid
planetary orbits of the Solar System. We describe the most important dynamical
processes in fully-formed planetary systems and how they are modeled. Such
methods have been applied to detect the evolution of exoplanet orbits in action
and to infer dramatic histories from the dynamical properties of planetary
systems.
