The present state of the theory of spin waves in magnetic insulators is reviewed. Special emphasis is placed on systems with an arbitrary site spin. Some illustrative calculations are carried out on the magnetic characteristics of several systems with a low density of particles (magnons) which interact strongly with each other. The distinctive features of reduced-dimensionality systems which stem from the governing role of spin fluctuations are examined. A separate chapter is devoted to magnetic phase transitions, primarily orientational. Several effects which stem from the dipole interaction of spins are also discussed.