We regard the Heisenberg model, the Hubbard model, the tJ‐model and the sd‐model as the basic models of the quantum theory of magnetism in solids. They can describe localized and itinerant magnets and strongly correlated electron systems. This review is devoted to analytical approaches for these models: diagrammatic techniques and the method of generating functional. The diagrammatic techniques are based on a generalization of the Wick theorem for spin andXoperators. Peculiarities of such techniques for the basic models appear because the spin andXoperators do not commute on aC‐value, but their commutator (anticommutator) is an operator itself. The method of generating functional is a generalization of the Kadanoff‐Baym approach, developed earlier for usual Fermi systems. The generating functional describes the interaction of a system with fluctuating fields, and different Green’s functions can be treated as variational derivatives with respect to these fields. Such approach allows to derive the equation of motion for the Green’s functions in each model in terms of functional derivatives. These equations help to find common features in the behavior of the basic models, particularly in finding the multiplicative structure of one‐particle Green’s functions. Iteration of the equations generates perturbation theory, which is compared with the diagrammatic techniques. Both approaches are applied to the calculation of the quasiparticle spectrum of the models and of collective excitations. A generalized random phase approximation (GRPA) is suggested for calculation of different dynamical susceptibilities. This approximation is developed in both approaches: the diagrammatic technique and the generating functional method. © 2003 American Institute of Physics