Migration type III Migration of objects embedded in disks (and the accompanying eccentricity evolution) is becoming a major theme in planetary system formation. The underlying physics can be distilled into the notion of disk-planet coupling via Lindblad resonances, which launch waves, sometimes spectacular spiral shock waves in gas disks. The wave pattern exchanges angular momentum with the planet. That causes (i) migration, (ii) eccentricity evolution, and (iii) gap opening by sufficiently massive planets. A competing source of disk-planet interaction, the corotational torques, are much less conspicuous (corotation does not produce easily detectable waves, as galaxy observers can attest) and have often been missed in the analysis of planet migration. If spiral waves are like waves at Goleta beach, then the corotation acts more like a stealthy riptide. Corotational flows lie at the basis of a new, surprisingly rapid, mode of migration (type III), superseding the standard type II migration (with a gap), and revising the speed of type I migration (without a gap). The talk will contain results obtained at KITP, e.g., an analytical derivation of da/dt in type III motion. It will be illustrated by videos of high-resolution numerical simulations obtained with different implementations of the Piecewise Parabolic Method hydrodynamics.