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In this paper we discuss experimental evidence related to the structure and origin of the bosonic spectral function α²F(ω) in high‐temperature superconducting (HTSC) cuprates at and near optimal doping. Global properties of α²F(ω), such as number and positions of peaks, are extracted by combining optics, neutron scattering, ARPES and tunnelling measurements. These methods give evidence for strong electron‐phonon interaction (EPI) with 1 < λ_ep≲3.5 in cuprates near optimal doping. We clarify how these results are in favor of the modified Migdal‐Eliashberg (ME) theory for HTSC cuprates near optimal doping. In Section 2 we discuss theoretical ingredients—such as strong EPI, strong correlations—which are necessary to explain the mechanism of d‐wave pairing in optimally doped cuprates. These comprise the ME theory for EPI in strongly correlated systems which give rise to the forward scattering peak …