A review of new developments in theoretical and experimental electronic-structure investigations of half-metallic ferromagnets (HMFs) is presented. Being semiconductors for one spin projection and metals for another, these substances are promising magnetic materials for applications in spintronics (i.e., spin-dependent electronics). Classification of HMFs by the peculiarities of their electronic structure and chemical bonding is discussed. The effects of electron-magnon interaction in HMFs and their manifestations in magnetic, spectral, thermodynamic, and transport properties are considered. Special attention is paid to the appearance of nonquasiparticle states in the energy gap, which provide an instructive example of essentially many-body features in the electronic structure. State-of-the-art electronic calculations for correlated $d$-systems are discussed, and results for specific HMFs (Heusler alloys, zinc-blende structure compounds, ${\mathrm{CrO}}_2$, and ${\mathrm{Fe}}_3{\mathrm{O}}_4$) are reviewed.

The versions of the self-consistent spin-wave theories (SSWT) of two-dimensional Heisenberg ferro- and antiferromagnets with a weak interlayer coupling and/or magnetic anisotropy, that are based on the nonlinear Dyson-Maleev, Schwinger, and combined boson-pseudofermion representations, are analyzed. Analytical results for the temperature dependences of (sublattice) magnetization and the short-range order parameter, and the critical points are obtained. The influence of external magnetic field is considered. Fluctuation corrections to SSWT are calculated within a random-phase approximation which takes into account correctly leading and next-leading logarithmic singularities. These corrections are demonstrated to improve radically the agreement with experimental data on layered perovskites and other systems. Thus an account of these fluctuations provides a quantitative theory of layered magnets.

The pinning of the Fermi level to the Van Hove singularity and the formation of flat bands in the two-dimensional $t-t^{\prime }$ Hubbard model is investigated by the renormalization group technique. The “Van Hove” scenario of non-Fermi-liquid behavior for high-$T_c$ compounds can take place in a broad enough range of the hole concentrations. The results are in qualitative agreement with the recent angle-resolved photoemission spectroscopy data on $\mathrm{L}{\mathrm{a}}_2\mathrm{C}\mathrm{u}{\mathrm{O}}_4$.

The $t-t^{\prime }$ Hubbard model for the Fermi level near the van Hove singularity is considered within the renormalization group and parquet approaches. Interplay of ferromagnetic, antiferromagnetic, and superconducting channels is investigated, and the phase diagram of the model is constructed. In comparison with previous approaches, the account of ferromagnetic fluctuations suppresses superconducting pairing and, vice versa, the influence of the Cooper channel decreases the Curie temperature, so that the Stoner criterion is inapplicable even qualitatively.

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Electron and spin Green functions of a Hubbard ferromagnet are calculated, both starting from the Stoner ground state and for a ferromagnet with Hubbard subbands. The temperature dependences of the spin-wave stiffness and damping, the magnetisation, the local moment on a site and the thermodynamic properties are investigated. The role of non-quasiparticle contributions, described by branch cuts of electron Green functions, is discussed. The non-quasiparticle ('ferrospinon') correction to the linear term in the specific heat is obtained. Experimental data on 'half-metallic' ferromagnets (in particular, spin polarisation and longitudinal nuclear relaxation rate) are analysed.