Gravitational torques between a planet and gas in the protoplanetary disk result in orbital migration of the planet, and modification of the disk surface density. Migration via this mechanism is likely to play an important role in the formation and early evolution of planetary systems. For masses comparable to those of observed giant extrasolar planets, the interaction with the disk is strong enough to form a gap, leading to coupled evolution of the planet and disk on a viscous time scale (Type II migration). Both the existence of hot Jupiters and the statistical distribution of observed orbital radii are consistent with an important role for Type II migration in the history of currently observed systems. We discuss the possibility of improving constraints on migration by including information on the host stars' metallicity, and note that migration could also form a population of massive planets at large orbital radii that may be indirectly detected via their influence on debris disks. For lower mass planets with Mp ~ M⊕, surface density perturbations created by the planet are small, and migration in a laminar disk is driven by an intrinsic and apparently robust asymmetry between interior and exterior torques. Analytic and numerical calculations of this Type I migration are in reasonable accord, and predict rapid orbital decay during the final stages of the formation of giant planet cores.