In many branches of physics, a standard model serves to explain and codify the existing body of experimental information and to allow predictions of novel phenomena. In the field of rare earth magnetism, such a model was constructed in the 1950s and ‘60s and has since been developed to an increasing level of completeness and sophistication. Its essential elements are a description of the states of the 4f electrons in rare earth materials and of their interactions with the surrounding crystal. Thus, the number of 4f electrons on each rare earth ion is taken to be integral, and their angular-momentum states are assumed to be the same as in the free atom. These localized states interact with their surroundings through, for example, the single-ion crystal-field and magnetoelastic forces, and with each other via the classical dipolar coupling and the indirect exchange interaction. In the latter, the 4f moments are coupled through the medium of the conduction electrons, which act as a passive transmitter, whose role is described by a static non-local susceptibility. Their dynamics have only a secondary function. A variety of theoretical techniques, among which the mean-field theory and its time-dependent extension, the random-phase approximation, are the most widely applicable, then allow the calculation of the magnetic properties in terms of well-defined parameters.