Relative to single-band models, multiband models of strongly interacting
electron systems are of growing interest because of their wider range of novel phenomena
and their closer match to the electronic structure of real materials. In this brief review
we discuss the physics of three multiband models (the three-band Hubbard, the periodic
Anderson, and the Falicov-Kimball models) that was obtained by numerical simulations
at zero temperature. We first give heuristic descriptions of the three principal numerical
methods (the Lanczos, the density matrix renormalization group, and the constrained-path Monte Carlo methods). We then present generalized versions of the models and
discuss the measurables most often associated with them. Finally, we summarize the
results of their ground state numerical studies. While each model was developed to study
specific phenomena, unexpected phenomena, usually of a subtle quantum mechanical
nature, are often exhibited. Just as often, the predictions of the numerical simulations
differ from those of mean-field theories.