The physical principles and basic theses of the theory, enabling a unified description of the magnetic properties of all thermodynamically stable domain structures in magnets, are presented. The theory is based on the following proposition proved by the authors: a necessary condition for the formation of all thermodynamically stable domain structures in magnets is the existence of a first-order phase transition induced by an external magnetic field. The approach developed makes it possible to regard the physics of domain structures as a part of thermodynamics, to derive the conditions for the existence of domains with different number of phases, to study the structure of the region of existence of domains, and to formulate for magnets with a domain structure an analogue of Gibbs rule. The general assertions of the theory are amply illustrated with experimental results. The properties of domain structures are analyzed in detail, and an interpretation is given for many experimental results for the most studied spin-reorientational transitions.