The goal of this project is to find the simplest atmospheric model that captures the essential physics of the dynamics of long-lived planetary features such as Jupiter's Great Red Spot and other coherent vortices, the Dark Spot of Neptune, the polar vortex of Saturn, and the Earth's Antarctic polar vortex. The philosophy is that a simple, but qualitatively correct model is the key to a good physical understanding of the mechanisms that govern planetary vortices, their wakes, and their waves.