  We give a definition of the notion of spherical varieties in the world of
complex supervarieties with actions of algebraic supergroups. A
characterization of affine spherical supervarieties is given which generalizes
a characterization in the classical case. We also explain some general
properties of the monoid of highest weights. Several examples are given that
are interesting in their own right and highlight differences with the classical
case, including the regular representation, symmetric supervarieties, and
actions of split supergroups.
