We have entered a new era in the observational study of the kinematics of dwarf spheroidal and dwarf elliptical galaxies. Large telescopes with multi-object spectrographs can now obtain radial velocities of hundreds if not thousands of individual stars in the nearer dSph systems, while new sensitive longslit spectrometers can measure the kinematics of dE galaxies from their integrated light to unprecedented faint surface brightness levels. I review where we have been, where we are, and where we are going in the kinematic studies of these dwarfs systems.