Surgical robots have greatly facilitated numerous challenging medical procedures such as totally endoscopic coronary artery bypass grafting. Despite the initial success of some classical robotic mechanisms (e.g., the da Vinci robot from Intuitive Surgical), limitations in the fundamental hardware impose constraints on the system capabilities and ease of use. While sensing, control, and computation hardware for robotically assisted surgery continue to improve, actuator technology remains relatively unchanged. This paper reviews the state of the art in actuators for surgical robotic devices and therefore elucidates the need for further actuator technology development. A physics-based actuator taxonomy is presented followed by a classification of the prominent research areas in surgical robotics. Using this taxonomic framework, we review the present role of actuator technology in surgical robotic devices.