By designing and implementing a new experimental method, we have measured the dynamic advancing and receding contact angles and the resulting hysteresis of droplets under electrowetting-on-dielectric (EWOD). Measurements were obtained over wide ranges of applied EWOD voltages, or electrowetting numbers (0 <= Ew <= 0.9), and droplet sliding speeds, or capillary numbers (1.4 x 10(-5) <= Ca <= 6.9 x 10(-3)). If Ew or Ca is low, dynamic contact angle hysteresis is not affected much by the EWOD voltage or the sliding speed; that is, the hysteresis increases by less than 50% with a 2 order-of-magnitude increase in sliding speed when Ca < 10(-3). If both Ew and Ca are high, however, the hysteresis increases with either the EWOD voltage or the sliding speed. Stick-slip oscillations were observed at Ew > 0.4. Data are interpreted with simplified hydrodynamic (Cox-Voinov) and molecular-kinetic theory (MKT) models; the Cox-Voinov model captures the trend of the data, but it yields unreasonable fitting parameters. MKT fitting parameters associated with the advancing contact line are reasonable, but a lack of symmetry indicates that a more intricate model is required.