  We briefly overview the importance of Hubbard and Anderson-lattice models as
applied to explanation of high-temperature and heavy-fermion superconductivity.
Application of the models during the last two decades provided an explanation
of the paired states in correlated fermion systems and thus extended
essentially their earlier usage to the description of itinerant magnetism,
fluctuating valence, and the metal-insulator transition. In second part, we
also present some of the new results concerning the unconventional
superconductivity and obtained very recently in our group. A comparison with
experiment is also discussed, but the main emphasis is put on rationalization
of the superconducting properties of those materials within the real-space
pairing mechanism based on either kinetic exchange and/or Kondo-type
interaction combined with the electron correlation effects.
