Description: A microscopic theory of spin excitations in strongly-correlated electronic systems within the t-J model is discussed. An exact representation for the dynamic spin susceptibility is derived. In the normal state, the excitation spectrum reveals a crossover from spin-wave-like excitations at low doping to overdamped paramagnons above the optimal doping. At low temperatures, the resonance mode at the antiferromagnetic wave vector Q = pi(1,1) emerges which is explained by a strong suppression of the spin excitation damping caused by a spin gap at Q rather than by opening of a superconducting gap. A major role of spin excitations in the d-wave superconducting pairing in cuprates is stressed in discussing mechanisms of high-Tc superconductivity within the Hubbard model in the limit of strong correlations, while electron-phonon interaction and a well-screened weak Coulomb interaction are not essential.