The spin-one-half Falicov–Kimball model for electronically driven valence and metal–insulator transitions is studied in one and two dimensions using small-cluster exact-diagonalization calculations. Performing an exhaustive study of the model close to the metal–insulator transition we have found that the spin-one-half Falicov–Kimball model can describe much of experimental data of transition-metal and rare-earth compounds. Particularly, except the discontinuous transitions it can provide the qualitative explanation for all typical behaviors of the electrical conductivity observed experimentally in these materials.