'l'he electf.'on ··phonon interaction bar; ed on the harm::>nicrnapprox.imati.on for phonons is discussed by considering severalrnphysical. models. Some consequences of t.his interaction I suchrnas the possibility of cooper pairing and the BCS theory ofrnsuperconductiv:lty are described.rnT'IO proposed mechanisms of High-Trncrnsuperconductivityrnboth based on the electron-ion interaction of electron pairingrnare discussed. II 2D BCS model results the observed values ofrnTand the absence of the isotope effect in its conventional crnform. Another model based on the non harmonic double-wellrnpotentials in the cu-o chain in YBCO is also studied. Arnqualitative prediction of the effect of pressure on Tc and thernsmallness of the critical current is made