  Strongly correlated Fermi systems are fundamental systems in physics that are
best studied experimentally, which until very recently have lacked theoretical
explanations. This review discusses the construction of a theory and the
analysis of phenomena occurring in strongly correlated Fermi systems such as
heavy-fermion (HF) metals and two-dimensional (2D) Fermi systems. It is shown
that the basic properties and the scaling behavior of HF metals can be
described within the framework of a fermion condensation quantum phase
transition (FCQPT) and extended quasiparticle paradigm that allow us to explain
the non-Fermi liquid behavior observed in strongly correlated Fermi systems. In
contrast to the Landau paradigm stating that the quasiparticle effective mass
is a constant, the effective mass of new quasiparticles strongly depends on
temperature, magnetic field, pressure, and other parameters. Having analyzed
collected facts on strongly correlated Fermi systems with quite different
microscopic nature, we find these to exhibit the same non-Fermi liquid behavior
at FCQPT. We show both analytically and using arguments based entirely on the
experimental grounds that the data collected on very different strongly
correlated Fermi systems have a universal scaling behavior, and materials with
strongly correlated fermions can unexpectedly be uniform in their diversity.
Our analysis of strongly correlated systems such as HF metals and 2D Fermi
systems is in the context of salient experimental results. Our calculations of
the non-Fermi liquid behavior, the scales and thermodynamic, relaxation and
transport properties are in good agreement with experimental facts.
