  We give a summary of joint work with Michael Thaddeus that realizes toroidal
compactifcations of split reductive groups as moduli spaces of framed bundles
on chains of rational curves. We include an extension of this work that covers
Artin stacks with good moduli spaces. We discuss, for complex groups, the
symplectic counterpart of these compactifications, and conclude with some open
problems about the moduli problem concerned.
