  This review aims at proposing to the field an overview of the Cusp-core
problem, including a discussion of its advocated solutions, assessing how each
can satisfactorily provide a description of central densities. Whether the
Cusp-core problem reflects our insufficient grasp on the nature of dark matter,
of gravity, on the impact of baryonic interactions with dark matter at those
scales, as included in semi-analytical models or fully numerical codes, the
solutions to it can point either to the need for a paradigm change in
cosmology, or to to our lack of success in ironing out the finer details of the
$\Lambda$CDM paradigm.
