Theoretical and experimental investigations of nuclear magnetic resonance in rare-earth Van Vleck paramagnetic materials are reviewed. The majority of the observed aspects of the phenomenon is explained by the interaction of nuclei with the residual electronic magnetic moment in the singlet ground state and the modulation of this interaction as a result of the coupling of the electronic moments among themselves and with the oscillations of the crystal lattice, and also by various spin-spin interactions involving enhanced nuclear moments. At liquid helium and higher temperatures the most significant effect is the modulation of the hyperfine interaction resulting from real thermal transitions of Van Vleck ions between the ground state and the nearest excited states. Within the framework of a single simple theory based on the randomly varying in time hyperfine interaction Hamiltonian, a description is given of the temperature dependence of the shifts and widths of NMR lines, of the spin-lattice relaxation times of nuclei within Van Vleck ions and within diamagnetic atoms, and also of the frequency and orientation dependences of these quantities. The theory is in agreement with experiment not only qualitatively, but to a significant extent also quantitatively without resorting to any adjustable parameters. Some special features of nuclear magnetism of Van Vleck paramagnetic materials at ultralow temperatures are also considered.