Abstract: The Falicov-Kimball model and its ground-state and low-temperature properties are shortly reviewed. The modifications of the model (the inclusion of the correlated hopping and next-nearest-neighbour hopping) are described, and their influence on ground state, as well as low-temperature properties are discussed. All models are studied in perturbative regime, i.e. for the case when the quotient of all hopping constants and Coulomb on-site repulsion is sufficiently small.