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My most recent work in [28] attempts to bring together the theory of asymptotics, singularity theory (encoded by a certain variety attached to each representation) and generalizations of classical Whittaker functions. The underlying techniques are analytic, algebraic and geometric. To each irreducible representation of interest, we can naturally associate a variety in g* (the dual of the Lie algebra), which is the closure of a single nilpotent orbit. My book [27], co-authored with Monty McGovern, lays out the theory of nilpotent orbits on a level accessible to interested graduate students. In fact, this book grew out of a two quarter course we taught at the University of Washington.