Abstract 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 ie no tolmachev morel anderson logarithm reducing the coulomb repulsion e ph interactions should be relatively . The observation of high temperature superconductivity in complex layered cuprates by bednorz and muller must now rate as one of the greatest experimental discoveries of the last century identifyin. Traditionally strong coupling superconductivity is understood as superconductivity induced by a very strong phonon mediated pairing interaction the strong coupling theory was developed by eliashberg21 on the basis of migdals theory for the normal state 43 in strong coupling superconductors the transition temperature tc is compa. The pairing theory of superconductivity is extended to treat systems having strong electron phonon coupling in this regime the landau quasiparticle approximation is invalid in the theory we