  High-temperature superconductivity (HTS) of cuprates represents a challenge
to the conventional theory. Here I review a multi-polaron approach to the
problem based on our extension of the BCS theory to the strong-coupling regime.
Since there is almost no retardation (i.e. no Tolmachev-Morel-Anderson
logarithm) reducing the Coulomb repulsion, e-ph interactions should be
relatively strong to overcome the direct Coulomb repulsion, so carriers must be
polaronic to form pairs in novel superconductors. I identify the Froehlich
electron-phonon interaction as the most essential for pairing in
superconducting cuprates, and discuss the "Froehlich-Coulomb" model of HTS,
low-energy structures, and the phase diagram of cuprates. "Individual" versus
Cooper pairing, normal state properties, in particular in-plane resistivity,
the Hall effect, magnetic susceptibility, the Lorenz number, the Nernst effect,
diamagnetism, spin and charge pseudogaps, and c-axis transport are also
discussed. I present a parameter-free evaluation of Tc, an explanation of
isotope effects, specific heat anomalies, upper critical fields, symmetries and
space modulations of the order parameter. Finally I introduce a model of
overdoped cuprates as mixtures of mobile bipolarons and degenerate lattice
polarons.
