  It has been now over 20 years since the discovery of the first high
temperature superconductor by Georg Bednorz and Alex Mueller in 1986 and yet,
despite intensive effort, no universally accepted theory exists about the
origin of high-temperature superconductivity. A controversial issue on whether
the electron-phonon interaction (EPI) is crucial for high-temperature
superconductivity or weak and inessential has been one of the most challenging
problems of contemporary condensed matter physics. I briefly review our recent
theoretical results, which in conjunction with a great number of experimental
observations including isotope effects, angle-resolved photoemission (ARPES),
pumpprobe and tunnelling spectroscopies, normal state diamagnetism and magnetic
quantum oscillations provide the definite answer to this fundamental question.
The true origin of high-temperature superconductivity is found in a significant
finite-range Froehlich EPI of nonadibatic polaronic carriers which is beyond
the conventional BCS-Migdal-Eliashberg approximation.
