The discovery of high-temperature superconductivity in copper oxides was not accidental, but was based on the knowledge that the divalent copper ion, Cu2+, is one of the strongest Jahn–Teller ions. The Jahn–Teller effect is a consequence of the interplay between electronic degeneracy and coupling to the lattice, i.e. unconventional local electron–lattice interactions. The search for superconductivity in copper oxides was motivated by the idea that Jahn–Teller polaron formation could be a novel and much stronger glue for electron pairing than conventional Bardeen–Cooper–Schrieffer electron–phonon coupling. The consequences of these ideas are unconventional isotope effects and complex pairing symmetries related to multiband superconductivity, which are reviewed here.