  A treatment of many-electron polar and $s-d(f)$ exchange models is carried
out in connection with the development of the theory of magnetism of transition
and rare-earth metals, as well as their compounds. Particular emphasis is
placed on the derivation of the many-electron Heisenberg, Hubbard, Anderson and
$t-J$ models, as well as the internal relationship between them. Among the
topics discussed are many-electron approaches in describing systems of $d$- and
$f$-electrons, atomic representation of Hubbard's $X$-operators, slave-particle
representations, the problem of strong itinerant magnetism and the formation of
local moments, the role of non-quasiparticle (incoherent states). The
application of these concepts to strongly correlated systems, in particular, to
half-metallic ferromagnets and Kondo lattices, is discussed. A comparison is
performed with modern field-theoretical and topological approaches.
