  Let G be a complex reductive group. A normal G-variety X is called spherical
if a Borel subgroup of G has a dense orbit in X. Of particular interest are
spherical varieties which are smooth and affine since they form local models
for multiplicity free Hamiltonian K-manifolds, K a maximal compact subgroup of
G. In this paper, we classify all smooth affine spherical varieties up to
coverings, central tori, and C*-fibrations.
