  Whittaker modules have been well studied in the setting of complex semisimple
Lie algebras. Their definition can easily be generalized to certain other Lie
algebras with triangular decomposition, including the Virasoro algebra. We
define Whittaker modules for the Virasoro algebra and obtain analogues to
several results from the classical setting, including a classification of
simple Whittaker modules by central characters and composition series for
general Whittaker modules.
