<p>Robotic surgery has the potential to fundamentally change interventional medicine by combining the complementary strengths of humans and machines. This can enhance safety as robots begin to intelligently interact with surgeons during training and to intra-operatively assist at varying levels of control and autonomy. In parallel, miniaturization is advancing the frontiers of how deeply robots can reach into the human body, and ergonomic user interfaces are improving the ability of surgeons to direct them. Improvements in tissue modelling, real-time feedback and delivery of diverse energy sources are key drivers of practical, intelligent human–machine collaborative systems. In this Review, we discuss the design and application of robotic systems in surgical procedures, outlining key elements in computer-assisted robotic surgery. Surgical robots are categorized based on the level of control and autonomy as passive, interactive, teleoperated and autonomous platforms. We conclude by discussing future milestones and current research frontiers in the engineering and clinical domain of surgical robotic systems.</p>