  Basic experimental facts related to ARPES, tunnelling, optics ad neutron
scattering measurements are discussed. They give evidence for the relevance of
the electron-phonon interaction (EPI) in pairing mechanism of HTSC cuprates. A
controllable theory for strong correlations and their effects on EPI is
discussed which is based on the 1/N expansion method in the t-J model. Strong
correlations renormalize EPI and other charge-fluctuation properties (by
including nonmagnetic impurity scattering) and the forward scattering peak
(FSP) appears in the effective interactions. Pronounced FSP in EPI of HTSC
cuprates reconciles many puzzling results. The theory of EPI with FSP gives
that the couplings in the s- and d-wave pairing channel are of the same
magnitude near and below the optimal hole doping. FSP in the nonmagnetic
impurity scattering potential is responsible for robustness of d-wave pairing
in cuprates. The ARPES kink and the isotope effect in the nodal and anti-nodal
points and the collapse of the elastic impurity scattering in the
superconducting state, are explained by this theory. It also explains why the
nodal kink is not-shifted in the superconducting state while the anti-nodal
kink is shifted by the maximal superconducting gap. In systems with FSP in EPI
besides the classical phase fluctuations there are also internal fluctuations
of Cooper pairs giving rise to an additional contribution to the pseudogap.
