When interpreted within the standard framework of Newtonian gravity and dynamics, the kinematics of stars and gas in dwarf galaxies reveals that most of these systems are completely dominated by their dark matter halos. These dwarf galaxies are thus among the best astrophysical laboratories to study the structure of dark halos and the nature of dark matter. We review the properties of the dwarf galaxies of the Local Group from the point of view of stellar dynamics. After describing the observed kinematics of their stellar components and providing an overview of the dynamical modelling techniques, we look into the dark matter content and distribution of these galaxies, as inferred from the combination of observed data and dynamical models. We also briefly touch upon the prospects of using nearby dwarf galaxies as targets for indirect detection of dark matter via annihilation or decay emission.