  In this document, I present a personal view on the heavy-fermion problem,
within a phenomenological approach guided by experiments. This review presents
a set of 'historical' works which established the ground bases of the thematic
during the last decades. An exhaustive and systematic approach is privileged.
After a general presentation in Chapter 2, the properties of heavy-fermion
paramagnets, antiferromagnets, and ferromagnets are considered in Chapters 3,
4, and 5, respectively. Chapters 6 and 7 are dedicated to two specific
compounds, URu$_2$Si$_2$ for which a 'hidden-order' phase constitutes a
more-than-thirty-years-old unsolved mystery, and UTe$_2$, where multiple
superconducting phases have been discovered in the last two years. Experiments
performed using a panel of techniques ranging from microscopic (neutron
scattering, NMR, etc.) to thermodynamic (specific heat, magnetization, etc.)
and transport (electrical resistivity, etc.) probes, under extreme conditions
of low temperatures, intense magnetic fields and high pressures, are reviewed.
They show that magnetism plays a central role in the quantum critical
properties of heavy-fermion systems. An emphasis is given to the intersite
magnetic fluctuations, presented as the driving force for a heavy Fermi liquid,
precursor of quantum magnetic criticality ending in magnetically-ordered
phases. They are also suspected to drive an unconventional mechanism for
superconductivity, which develops in the vicinity of quantum magnetic phase
transitions induced under pressure or magnetic field. The appearance of
magnetic fluctuations and ultimately magnetic order in heavy-fermion compounds
occurs in a nearly-integer-valence regime, in which $f$ electrons have a dual
itinerant-localized character. Fermi-surface and valence studies, which give
complementary information about this duality, are also considered.
