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The way in which nonstoichiometry and order and disorder interrelate in solid phase compounds is discussed. Nonstoichiometry due to the presence of structural vacancies is widely found in such solid phase compounds as transition metal carbides, nitrides, and oxides, and in related ternary interstitial compounds. It is shown that it is nonstoichiometry that determines the disordered or ordered distribution of atoms and vacancies. A review is given of the current status of research into structural order-disorder phase transitions in nonstoichiometric compounds with basal cubic and hexagonal crystal lattices. Symmetry analysis results for disorder-order and order-order phase transformations are considered in detail. Key superstructure types that form in nonstoichiometric compounds with vacancies in one or two sublattices are also described.