  QCD possesses a compact gauge group, and this implies a non-trivial
topological structure of the vacuum. In this contribution to the Gribov-85
Memorial volume, we first discuss the origin of Gribov copies and their
interpretation in terms of fluctuating topology in the QCD vacuum. We then
describe the recent work with E. Levin that links the confinement of gluons and
color screening to the fluctuating topology, and discuss implications for spin
physics, high energy scattering, and the physics of quark-gluon plasma.
