  In this article, we investigate the geometry of reductive group actions on
algebraic varieties. Given a connected reductive group $G$, we elaborate on a
geometric and combinatorial approach based on Luna-Vust theory to describe
every normal $G$-variety with spherical orbits. This description encompasses
the classical case of spherical varieties and the theory of
$\mathbb{T}$-varieties recently introduced by Altmann, Hausen, and S\"uss.
