2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161486High-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.65 pages, 24 figures, 187 references, invited review to the Special Golden Jubilee volume of Studies of High-Temperature Superconductors, ed. A. Narlikar, typos correctedSuperconductivityStrongly Correlated Electronstext