  Let $X$ be a variety with an action by an algebraic group $G$. In this paper
we discuss various properties of $G$-equivariant $D$-modules on $X$, such as
the decompositions of their global sections as representations of $G$ (when $G$
is reductive), and descriptions of the categories that they form. When $G$ acts
on $X$ with finitely many orbits, the category of equivariant $D$-modules is
isomorphic to the category of finite-dimensional representations of a finite
quiver with relations. We describe explicitly these categories for irreducible
$G$-modules $X$ that are spherical varieties, and show that in such cases the
quivers are almost always representation-finite (i.e. with finitely many
indecomposable representations).
