Theoretical studies of the spin fluctuation spectrum and superconducti
ng pairing mediated by spin fluctuation exchange are reported with a s
pecial emphasis on the results obtained for microscopic models with st
rong electron correlations: the one-band Hubbard model and the t-J mod
el. Phenomenological models for spin fluctuation pairing are also cons
idered. The symmetry of the superconducting order parameter and the do
ping dependence of superconducting transition temperature T-c obtained
by numerical solutions of the strong-coupling Eliashberg equations fo
r the microscopic models are discussed. The theoretical investigations
presented strongly support the spin-exchange pairing mechanism in cop
per oxides.