The desire for functional replacement of a missing hand is an ancient one. Historically, humans have replaced a missing limb with a prosthesis for cosmetic, vocational, or personal autonomy reasons. The hand is a powerful tool, and its loss causes severe physical and often mental debilitation. Technological advancements have allowed the development of increasingly effective artificial hands, which can improve the quality of life of people who suffered a hand amputation. Here, we review the state of the art of robotic prosthetic hands (RPHs), with particular attention to the potential and current limits of their main building blocks: the hand itself, approaches to decoding voluntary commands and controlling the hand, and systems and methods for providing sensory feedback to the user. We also briefly describe existing approaches to characterizing the performance of subjects using RPHs for grasping tasks and provide perspectives on the future of different components and the overall field of RPH development.