  In this review we present a biased review of the ground state properties of
the Falicov-Kimball models in 1,2 and infinite dimensions, considering either
fermions or hard-core bosons. In particular we want to show the very rich
structure that these models exhibit and to point out the analogies and
differences associated with the statistic of the quantum particles and the
nature of the lattice (bipartite or not). The flux phase problem is also
discussed.
