An overview of recent achievements of the disclination approach in mechanics and physics of solids is given and the use of disclination modeling in materials science is demonstrated. Disclinations are defined as linear defects in solids, which manifest themselves as the sources of characteristic singularities in the fields of displacement and rotation. Necessary terminilogy and designations: Volterra dislocations, Frank (rotation) vector of a disclination, wedge and twist disclinations, are provided and discussed. The properties of screened disclination configurations (loops, dipoles, defects in small particles, etc.) with relatively small energies are considered. The methods and results of calculation of elastic energies for screened disclinations (for example, near a free surface) are presented. On the basis of properties of screened disclinations a series of models for the processes in the structure of plastically deformed materials is developed. The bands with misorientated crystal lattice in metals and other materials are described as a result of partial wedge disclination dipole motion. Disclination models are applied to the analysis of workhardening at large strains and to the theory of grain boundaries and their junctions in polycrystals. Disclination models for the structure and properties of nanostructured materials and nanoparticles are also delivered. Finally, the role of disclinations in relaxation of elastic stresses in epitaxial thin films is highlighted.