On the basis of extensive studies of synthetic perovskite-structured compounds it is possible to derive a hierarchy of hettotype structures which are derivatives of the arisotypic cubic perovskite structure (ABX3), exemplified by SrTiO3 (tausonite) or KMgF3 (parascandolaite) by: (1) tilting and distortion of the BX6 octahedra; (2) ordering of A- and B-site cations; (3) formation of A-, B- or X-site vacancies. This hierarchical scheme can be applied to some naturally-occurring oxides, fluorides,hydroxides, chlorides, arsenides, intermetallic compounds and silicates which adopt such derivative crystal structures. Application of this hierarchical scheme to naturally-occurring minerals results in the recognition of a perovskite supergroup which is divided into stoichiometric and non-stoichiometricperovskite groups, with both groups further divided into single ABX3 or double A2BB'X6 perovskites. Subgroups, and potential subgroups, of stoichiometric perovskites include: (1) silicate single perovskites of the bridgmanite subgroup;(2) oxide single perovskites of the perovskite subgroup (tausonite, perovskite, loparite, lueshite, isolueshite, lakargiite, megawite); (3) oxide single perovskites of the macedonite subgroup which exhibit second order Jahn-Teller distortions (macedonite, barioperovskite); (4) fluoride singleperovskites of the neighborite subgroup (neighborite, parascandolaite); (5) chloride single perovskites of the chlorocalcite subgroup; (6) B-site cation ordered double fluoride perovskites of the cryolite subgroup (cryolite, elpasolite, simmonsite); (7) B-site cation orderedoxide double perovskites of the vapnikite subgroup [vapnikite, (?) latrappite]. Non-stoichiometric perovskites include: (1) A-site vacant double hydroxides, or hydroxide perovskites, belonging to the söhngeite, schoenfliesite and stottite subgroups; (2) Anion-deficient perovskitesof the brownmillerite subgroup (srebrodolskite, shulamitite); (3) A-site vacant quadruple perovskites (skutterudite subgroup); (4) B-site vacant single perovskites of the oskarssonite subgroup [oskarssonite]; (5) B-site vacant inverse single perovskites of the coheniteand auricupride subgroups; (6) B-site vacant double perovskites of the diaboleite subgroup; (7) anion-deficient partly-inverse B-site quadruple perovskites of the hematophanite subgroup.