  The electronic and magnetic properties of many strongly-correlated systems
are controlled by a limited number of states, located near the Fermi level and
well isolated from the rest of the spectrum. This opens a formal way for
combining the methods of first-principles electronic structure calculations,
based on the density-functional theory (DFT), with many-body models, formulated
in the restricted Hilbert space of states close to the Fermi level. The core of
this project is the so-called "realistic modeling" or the construction of the
model many-body Hamiltonians entirely from the first principles. Such a
construction should be able to go beyond the conventional local-density
approximation (LDA), which typically supplements the density-functional theory,
and incorporate the physics of Coulomb correlations. It should also provide a
transparent physical picture for the low-energy properties of strongly
correlated materials. In this review article, we will outline the basic ideas
of such a realistic modeling. The entire procedure will be illustrated on the
series of examples, including the distorted transition-metal perovskite oxides,
the compounds with the inversion symmetry breaking caused by the defects, and
the alkali hyperoxide KO2, which can be regarded as an analog of
strongly-correlated systems where the localized electrons reside on the
molecular orbitals of the O2- dimer. In order to illustrate abilities of the
realistic modeling, we will also consider solutions of the obtained low-energy
models for a number of systems, and argue that it can be used as a powerful
tool for the exploration and understanding of properties of strongly correlated
materials.

Strongly Correlated Electrons