Generalized and degenerate Whittaker quotients and Fourier coefficients

The study of Whittaker models for representations of reductive groups over local and global fields has become a central tool in representation theory and the theory of automorphic forms. However, only generic representations have Whittaker models. In order to encompass other representations, one attaches a degenerate (or a generalized) Whittaker model WO, or a Fourier coefficient in the global case, to any nilpotent orbit O. In this note we survey some classical and some recent work in this direction - for Archimedean, p-adic and global fields. The main results concern the existence of models. For a representation π, call the set of maximal orbits O with WO that includes π the Whittaker support of π. The two main questions discussed in this note are: (1) What kind of orbits can appear in the Whittaker support of a representation? (2) How does the Whittaker support of a given representation π relate to other invariants of π, such as its wave-front set?