The theoretical and experimental studies on the transition to dynamical chaos in magnetic systems are reviewed. Both dissipative and Hamiltonian systems are discussed, with their fundamental scenarios of the transition to chaos. We discuss the models and characteristics of chaotic oscillations in magnetic materials upon parametric excitation of spin waves, in NMR masers, in the dynamics of spin chains, in the motion of a spin in an external alternating magnetic field, and in nonlinear NMR with dynamic shift of the precession frequency. An analysis of the problems of quantum chaos in spin systems is presented.