  In this review we present results of our theoretical study of charge and spin
ordering in strongly correlated electron systems obtained within various
generalizations of the Falicov-Kimball model. The primary goal of this study
was to identify crucial interactions that lead to the stabilization of various
types of charge ordering in these systems, like the axial striped ordering,
diagonal striped ordering, phase-separated ordering, phase-segregated ordering,
etc. Among the major interactions that come into account, we have examined the
effect of local Coulomb interaction between localized and itinerant electrons,
long-range and correlated hopping of itinerant electrons, long-range Coulomb
interaction between localized and itinerant electrons, local Coulomb
interaction between itinerant electrons, local Coulomb interaction between
localized electrons, spin-dependent interaction between localized and itinerant
electrons, both for zero and nonzero temperatures, as well as for doped and
undoped systems. Finally, the relevance of resultant solutions for a
description of rare-earth and transition-metal compounds is discussed.
