We discuss some of the recently proposed models dealing with the super
conducting state in the presence of strong antiferromagnetic fluctuati
ons, induced by the on-site Coulomb repulsion between electrons (the H
ubbard correlation). In the weak coupling limit we treat the influence
of correlation effects on the phonon-mediated superconductivity withi
n the BCS-Eliashberg framework. As a non-standard model in this limit
we describe next the so-called spin bag model. To discuss strong corre
lation limit, we describe first the projected Hamiltonian (the t-J Ham
iltonian) and the corresponding antiferromagnetic state. The resonatin
g valence bond model is introduced both as a naive version, equivalent
to the BCS treatment of the transverse spin fluctuations, as well as
a holon-spinon version.