  A neutron star is pictured as a gigantic nucleus overwhelmed by the number of
neutrons, unlike real atomic nuclei, that have a similar number of neutrons and
protons. Is this true? What if we could find, or create nuclei without protons?
How far can we go in neutron richness? Our common sense tells us that these
neutral nuclei should not exist, but if they do they would change our knowledge
on neutron stars, on the properties of nuclei in general, and ultimately on the
nucleon-nucleon interaction itself, the building block of matter. This huge
potential impact has pushed some ambitious nuclear physicists to search for
them since the 1960s. The first positive hints appeared only in the XXI
century, and nowadays several collaborations are trying to corner these weird
objects and give a definite answer to this crucial question. In this
\edit{review} we will go through this fascinating quest, that started with
humble experiments and has now reached a stage of ambitious and sophisticated
projects, both in experiment and theory.
