  This review deals with the inconsistency of inner dark matter density
profiles in dwarf galaxies, known as the cusp-core problem. Particularly, we
aim to focus on gas-poor dwarf galaxies. One of the most promising solutions to
this cold dark matter small scale issue is the stellar feedback but it seems to
be only designed for gas-rich dwarfs. However, in the regime of classical
dwarfs, this core mechanism becomes negligible. Therefore, it is required to
find solutions without invoking these baryonic processes as dark matter cores
tend to persist even for these dwarfs, which are rather dark matter-dominated.
Here we have presented two categories of solutions. One consists of creating
dark matter cores from cusps within cold dark matter by altering the dark
matter potential via perturbers. The second category gathers solutions which
depict the natural emergence of dark matter cores in alternative theories.
Given the wide variety of solutions, it becomes necessary to identify which
mechanism dominates in the central region of galaxies by finding observational
signatures left by them in order to highlight the true nature of dark matter.
