Open systems that contain chemically reacting mixtures and are restrained from relaxation to thermodynamic equilibrium manifest a capability of characteristic collective effects. In particular, macroscopically ordered states (dissipative structures) can arise in them spontaneously. This study discusses the fundamental results of the theory of dissipative structures: potential multiplicity of states differing in type of spatial organization, the possibility of both spontaneous and induced transitions between these states, and a universal description of the dynamics of establishment of macroscopic order. The capability of self-organization of a broad set of physicochemical systems opens up the possibility of modeling processes of desymmetrization and complication of spatial organization during the embryonic development of multicellular organisms. The article reflects the most significant results in this field.