This review summarizes the results of studies of anisotropic magnetostriction in rare-earth and actinide magnetics. Experimental data are given on the magnetostrictive constants in the rare-earth metals, alloys, intermetallic compounds, garnet ferrites, various uranium compounds, etc. The nature of the giant magnetostriction observed in compounds of the rare earths and actinides is analyzed. This magnetostriction is shown in most cases to have a single-ion origin, and to be due to interaction of the orbital moment of the rare-earth (or actinide) ion with the crystal field of the lattice. The influence is discussed of the magnetoelastic interaction on the physical properties (magnetic anisotropy, elastic modulus, etc.) of rare-earth and actinide magnetics. The parameters of intermetallic compounds showing giant magnetostriction in the roomtemperature region and the possibilities of technical application are discussed.