  Buckminsterfullerene compounds exibit remarkable physics at low temperatures,
e.g. high temperature superconductivity in alkali-fullerenes, and
ferromagnetism in TDAE -C60. Here we review recent theoretical studies of
electron correlations in these compounds. In particular, we discuss models of
electron-vibron interactions, electron-electron interactions, and
intermolecular hopping. We show that the origin of novel electronic phases lies
in {\em local} degeneracies of C60; a direct consequence of the high molecular
symmetry.
