I review observational data on the kinematic properties of dwarf spheroidal galaxies in the halo of the Milky Way and beyond. The present data confirm previous claims that these galaxies have unusually large central velocity dispersions. `Simple' sources of bias such as binary stars, internal atmospheric motions, measurement errors, and small sample sizes cannot explain the large dispersions measures in all dSph systems. Recent data suggest that in some of these dwarfs the veolocity dispersion profiles are flat out to their classical tidal radii. I discuss how these results can (or cannot) be understood by invoking a variety of distinct models, including classical dark matter halos, tidal disruption and MOND.

10 pages, 2 figures; to appear in `The Nature of Elliptical Galaxies', eds. M. Arnabaldi, G. Da Costa, and P. Saha