The perovskites and perovskite-related structures exhibit several features of technical as well as fundamental interest. Technically useful properties include oxide-ion conduction with/without electronic conduction, oxidation catalysis, ferroic displacements in classic and relaxor ferroelectrics, half-metallic ferromagnetism and high-temperature superconductivity. Of more fundamental interest is the ability to tune, by chemical substitution on the large-cation subarray, transition-metal oxides through the crossover on the transition-metal array from localized dⁿ configurations to itinerant d-electron behaviour without/with changing the valence state of that array. The localized-electron configurations may exhibit cooperative Jahn–Teller distortions that introduce anisotropic exchange interactions. At crossover, bond-length fluctuations may segregate into an ordered array of alternating covalent and ionic bonding in a single-valent perovskite; multicentre polarons or correlation bags may replace small polarons in a mixed-valent system. Bond-length fluctuations at crossover give vibronic conduction and suppression of the phonon contribution to the thermal conductivity; the fluctuations may order, to give high-temperature superconductivity, or transform to quantum–critical-point behaviour at lowest temperatures. Crossover of σ-bonding electrons in the presence of localized spins associated with π-bonding electrons gives rise to the colossal magnetoresistance phenomenon above a ferromagnetic Curie temperature.