This review treats the little-studied magnetic phase transitions of the order-order, spin-reorientation type, in which a rotation of the magnetization vector (or of die antiferromagnetism vector) with respect to the crystallographic axes occurs upon change of temperature, magnetic field, or external pressure. It presents theoretical ideas about magnetic phase transitions of the spin-reorientation type; it considers the effect of domain structure on spin-reorientation phase transitions, aad critical fluctuations during such transitions. Taking as an example rare-earth magnets (orthoferrites, iron-garnets, and rare-earth metals and intermetallic compounds), it considers the experimental data on various types of spin-reorientation transitions and on the anomalies of physical properties at such transitions.