Abstract
A review of the antiferromagnetic exchange and spin-fluctuation pairing theory in the cuprate superconductors is given. We briefly discuss a phenomenological approach and a theory in the limit of weak Coulomb correlations. A microscopic theory in the strong correlation limit is presented in more detail. In particular, results of our recently developed theory for the effective p-d Hubbard model and the reduced t-J model are given. We have proved that retardation effects for the antiferromagnetic exchange interaction are unimportant, which results in pairing of all the charge carriers in the conduction band and a high Tc proportional to the Fermi energy. The spin-fluctuation interaction caused by kinematic interaction gives an additional contribution to the d-wave pairing. The dependence of Tc on the hole concentration and lattice constant (or pressure) and an oxygen isotope shift are discussed.
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