  In a short review-article we first discuss the results, which are mainly
devoted to the generalizations of the famous Kohn-Luttinger mechanism of
superconductivity in purely repulsive fermion systems at low electron
densities. In the context of repulsive-U Hubbard model and Shubin-Vonsovsky
model we consider briefly the superconducting phase diagrams and the symmetries
of the order parameter in novel strongly correlated electron systems including
idealized monolayer and bilayer graphene. We stress that purely repulsive
fermion systems are mainly the subject of unconventional low-temperature
superconductivity. To get the high temperature superconductivity in cuprates
(with T_C of the order of 100 K) we should proceed to the t-J model with the
Van der Waals interaction potential and the competition between short-range
repulsion and long-range attraction. Finally we stress that to describe
superconductivity in metallic hydrogen alloys under pressure (with T_C of the
order of 200 K) it is reasonable to reexamine more conventional mechanisms
connected with electron-phonon interaction. These mechanisms arise in the
attractive-U Hubbard model with static onsite or intersite attractive potential
or in more realistic theories (which include retardation effects) such as
Migdal-Eliashberg strong coupling theory or even Fermi-Bose mixture theory of
Ranninger et al., and its generalizations.
