Dwarf spheroidal galaxies are key objects in the current cosmological paradigm: first, they are the least luminous galaxies, likely signaling the minimum halo mass at which gas can be accreted and converted into stars. Second, they all have ancient stellar populations, providing clues on star formation/feedback processes at early stages of the Universe. Third, they are the most numerous satellites about the Milky Way and M31, helping us to uncover the hierarchical formation of galaxies. And fourth, they appear to be the most dark matter dominated galaxies in the known Universe, which allow us to directly test a number of different cosmological predictions. In this talk I will present the results of two recent papers where we use observational data to constrain the presence (or the lack thereof) of (i) dark matter cusps and (ii) dark substructures (also called "dark galaxies") in the haloes wherein dwarf galaxies are embedded.