We present a discussion of the present state of experimental and theoretical investigations of a new class of metallic systems based on f-shell elements: the class of nonmagnetic Kondo lattices, in which the low-temperature density of electron states at the Fermi level is 100--1000 times larger than in normal metals, as a consequence of the generation of an astonishingly narrow ($\sim$10$^\circ$K) Abrikosov--Suhl resonance of gigantic amplitude near the Fermi level. This resonance is related to the presence of quasiparticles with effective masses $m^*\sim$(10$^2$--10$^3$)$m_0$ -- ``heavy fermions''. We show that the overwhelming majority of ``heavy fermion systems'' are in fact nonmagnetic Kondo lattices. We analyze the unusual properties of heavy-fermion superconductors, and point out the nontrivial nature of superconductivity in these systems.