High-precision gravitational measurements by orbiting spacecraft provide a means of probing the structures, fluid motions, and convective dynamos in the interiors of the rapidly rotating outer planets. Here, the classical theory of rotating homogeneous planets is briefly reviewed. Emphasis is placed on recent developments in theories and methods that relate internal structure and processes to their gravitational signatures. Whereas early theories usually treated the effects of interior density stratification and rotational distortion as perturbations to a spherical state, recent research is marked by a self-consistent perturbation approach in which the leading-order problem accounts exactly for rotational distortion, thereby determining the basic shape, internal structure, and gravitational field of the planet. The next-order problem, which is mathematically and physically coupled with the leading-order problem, describes the modifications caused by internal fluid motions. Although the theories and methods have general applicability, advances have been spurred by the need to have a basis for interpretation of the gravitational data for Jupiter and Saturn expected from the Juno and Cassini missions.


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