Traditional rigid robot application in the medical field is limited due to the limited degrees of freedom caused by their material and structure. Inspired by trunk, tentacles, and snakes, continuum robot (CR) could traverse confined space, manipulate objects in complex environment, and conform to curvilinear paths in space. The continuum robot has broad prospect in surgery due to its high dexterity, which can reach circuitous areas of the body and perform precision surgery. Recently, many efforts have been done by researchers to improve the design and actuation methods of continuum robots. Several continuum robots have been applied in clinic surgical interventions and demonstrated superiorities to conventional rigid-link robots. In this paper, we provide an overview of the current development of continuum robots, including the design principles, actuation methods, application prospect, limitations, and challenge. And we also provide perspective for the future development. We hope that with the development of material science, Engineering ethics, and manufacture technology, new methods can be applied to manufacture continuum robots for specific surgical procedures.