  The complex nature of the nuclear forces generates a broad range and
diversity of observational phenomena. Heavy nuclei, though orders of magnitude
less massive than neutron stars, are governed by the same underlying physics,
which is enshrined in the nuclear equation of state. Heavy nuclei are expected
to develop a neutron-rich skin where many neutrons collect near the surface.
Such a skin thickness is strongly sensitive to the poorly-known density
dependence of the symmetry energy near saturation density. An accurate and
model-independent determination of the neutron-skin thickness of heavy nuclei
would provide a significant first constraint on the density dependence of the
nuclear symmetry energy. The determination of the neutron-skin thickness of
heavy nuclei has far reaching consequences in many areas of physics as diverse
as heavy-ion collisions, polarized electron and proton scattering off nuclei,
precision tests of the standard model using atomic parity violation, and
nuclear astrophysics. While a systematic and concerted experimental effort has
been made to measure the neutron-skin thickness of heavy nuclei, a precise and
model-independent determination remains elusive. How to move forward at a time
when many new facilities are being commissioned and how to strengthen the
synergy with other areas of physics are primary goals of this review.
