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We argue that the unusual properties of a wide class of materials based onJahn-Teller 3d and 4d ions with different crystal and electronic structures,from quasi-two-dimensional unconventional superconductors (cuprates,nickelates, ferropnictides/chalcogenides, ruthenate SrRuO4), manganites withlocal superconductivity to 3D ferrates (CaSr)FeO3, nickelates RNiO3 and silveroxide AgO with unusual charge and magnetic order can be explained within asingle scenario. The properties of these materials are related to theinstability of their highly symmetric Jahn-Teller "progenitors" with the groundorbital E-state to charge transfer with anti-Jahn-Teller disproportionation andthe formation of a system of effective local composite spin-singlet orspin-triplet, electronic or hole bosons moving in a non-magnetic or magneticlattice. These unusual systems are characterized by an extremely rich varietyof phase states from non-magnetic and magnetic insulators to unusual metallicand superconducting states.

Anti-Jahn-Teller disproportionation and prospects for spin-triplet superconductivity in d-element compounds