  We consider a random family of Schr\"odinger operators on a cover $X$ of a
compact Riemannian manifold $M = X/\Gamma$. We present several results on their
spectral theory, in particular almost sure constancy of the spectral components
and existence and non-randomness of an integrated density of states. We also
sketch a groupoid based general framework which allows to treat basic features
of random operators in different contexts in a unified way. Further topics of
research are also discussed.
