  The aim of this review paper is to expose a new state of matter exhibited by
strongly correlated Fermi systems represented by various heavy-fermion (HF)
metals, two-dimensional liquids like $\rm ^3He$, compounds with quantum spin
liquids, quasicrystals, and systems with one-dimensional quantum spin liquid.
We name these various systems HF compounds, since they exhibit the behavior
typical of HF metals. In HF compounds at zero temperature the unique phase
transition, dubbed throughout as the fermion condensation quantum phase
transition (FCQPT) can occur; this FCQPT creates flat bands which in turn lead
to the specific state, known as the fermion condensate. Unlimited increase of
the effective mass of quasiparticles signifies FCQPT; these quasiparticles
determine the thermodynamic, transport and relaxation properties of HF
compounds. Our discussion of numerous salient experimental data within the
framework of FCQPT resolves the mystery of the new state of matter. Thus, FCQPT
and the fermion condensation can be considered as the universal reason for the
non-Fermi liquid behavior observed in various HF compounds. We show
analytically and using arguments based completely on the experimental grounds
that these systems exhibit universal scaling behavior of their thermodynamic,
transport and relaxation properties. Therefore, the quantum physics of
different HF compounds is universal, and emerges regardless of the microscopic
structure of the compounds. This uniform behavior allows us to view it as the
main characteristic of a new state of matter exhibited by HF compounds.
