We review our current understanding of the internal dynamical properties of the dwarf spheroidal galaxies surrounding the Milky Way. These are the most dark matter dominated galaxies, and as such may be considered ideal laboratories to test the current concordance cosmological model, and in particular provide constraints on the nature of the dominant form of dark matter. We discuss the latest observations of the kinematics of stars in these systems, and how these may be used to derive their mass distribution. We tour through the various dynamical techniques used, with emphasis on the complementarity and limitations, and discuss what the results imply also in the context of cosmological models. Finally we provide an outlook on exciting developments in this field.

89 pages, 12 figures. Invited review article to be published in the special issue "Galactic Archaeology" of New Astronomy Reviews