We classify within the quasi-geostrophic framework all types of traveling waves in zonal bands of the planetary atmosphere at cloud level according to their wave speeds. This classification pertains to waves of all amplitudes, going beyond the small-amplitude perturbative regime. Each wave classification type was observed on Jupiter or Saturn. Building on this classification, we also give a thorough characterization of traveling waves near a monotone shear flow, and study the related rigidity issue for large-amplitude traveling waves. This is a joint work with Profs. Adrian Constantin and Zhiwu Lin.