If $G$ is a reductive group and $X$ a (normal) affine $G$-variety, we call $X$ spherical if every irreducible $G$-module occurs at most once in the coordinate ring $C[X]$ of $X$. Inspired by a conjecture of Friedrich Knop, which states that any such variety is determined by the module structure of $C[X]$, we classified the smooth affine spherical varieties up to coverings, central tori, and $C^*$-fibrations. We give an outline of the classification and briefly sketch the conjecture's origins in symplectic geometry: it is equivalent to Delzant's conjecture that compact multiplicity free Hamiltonian $K$-manifolds ($K$ a compact connected Lie group) are uniquely determined by their generic isotropy group and the image of the moment map.