The continued development of electro-hydrostatic actuators (EHAs) in aerospace applications has put forward an increasing demand upon EHA pumps for their high power density. Besides raising the delivery pressure, increasing the rotational speed is another effective way to achieve high power density of the pump, especially when the delivery pressure is limited by the strength of materials. However, high-speed operating conditions can lead to several challenges to the pump design. This paper reviews the current challenges including the cavitation, flow and pressure ripples, tilting motion of rotating group and heat problem, associated with a high-speed rotation. In addition, potential solutions to the challenges are summarized, and their advantages and limitations are analyzed in detail. Finally, future research trends in EHA pumps are suggested. It is hoped that this review can provide a full understanding of the speed limitations for EHA pumps and offer possible solutions to overcome them.