This review deals with the inconsistency of inner dark matter density profiles in dwarf galaxies, known as the cusp–core problem. In particular, 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 that 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.