In laboratory studies and associated theoretical and numerical work covering a very wide range of conditions (as specified by the key dimensionless parameters of the systems used) the phenomenon of sloping convection in rotating fluids can manifest itself in one of several spatial forms (waves, closed eddies, and combinations thereof), but all with strong local gradients (fronts, jet streams) and exhibiting various types of temporal behavior [steady, periodic vacillation, aperiodic (geostrophic) turbulence]. These general properties were first discovered in cylindrical (annular) systems, but they do not depend critically on geometry; differences between spherical and cylindrical systems are largely to be found in quantitative details. In all cases, the raison d'e tre of sloping convection is horizontal advective transfer, a process accompanied by upward advective heat transfer, which affects and may control vertical potential density gradients. It has been argued that sloping convection is the basic dynamical process underlying a wide variety of large-scale flow phenomena seen in planetary atmospheres (e.g., irregular waves in the Earth's atmosphere, regular waves in the Martian atmosphere, the Jovian Great Red Spot and other long-lived eddies seen in the atmospheres of the giant planets). In this review the extent to which this paradigm is upheld in the atmospheres of the major planets by recent work is discussed.