  In this review article we consider theoretically and give experimental
support to the models of the Fermi-Bose mixtures and the BCS-BEC crossover
compared with the strong-coupling approach, which can serve as the cornerstones
on the way from high-temperature to room-temperature superconductivity in
pressurized metallic hydrides. We discuss some key theoretical ideas and
mechanisms proposed for unconventional superconductors (cuprates, pnictides,
chalcogenides, bismuthates, diborides, heavy-fermions, organics, bilayer
graphene, twisted graphene, oxide hetero-structures), superfluids and balanced
or imbalanced ultracold Fermi gases in magnetic traps. We build a bridge
between unconventional superconductors and recently discovered pressurized
hydrides superconductors H3S and LaH10 with the critical temperature close to
room temperature. We discuss systems with line of nodal Dirac points close to
the Fermi surface, superconducting shape resonances and hyperbolic
superconducting networks which are very important for the development of novel
topological superconductors, for the energetics, for the applications in
nano-electronics and quantum computations.
