Dwarf spheroidal galaxies (dSphs) are the most dark matter (DM)–dominated galaxies in the Universe, and as such, they provide excellent targets for testing a wide range of DM theories. In this talk, I will review our current understanding of the amount and distribution of DM in these systems, as inferred from the kinematics of individual stars, and discuss whether or not current observations are in tension with Cold DM predictions. I will also focus on a key prediction of CDM theory: the existence of a large population of dark subhaloes orbiting within the DM haloes of dSphs, and how these invisible objects may perturb the internal stellar dynamics, offering new observational tests that will soon be accessible with forthcoming photometric and spectroscopic surveys of the Milky Way dSphs.