Current surgical devices are mostly rigid and are made of stiff materials, even though their predominant use is on soft and wet tissues. With the emergence of compliant mechanisms (CMs), surgical tools can be designed to be flexible and made using soft materials. CMs offer many advantages like monolithic fabrication, high precision, no wear, no friction and no need for lubrication. It is therefore beneficial to consolidate the developments in this field and point to challenges ahead. With this objective, in this paper, we review the application of CMs to surgical interventions. The scope of the review covers five aspects that are important in the development of surgical devices: (i) conceptual design and synthesis, (ii) analysis, (iii) materials, (iv) manufacturing, and (v) actuation. Furthermore, the surgical applications of CMs are assessed by classification into five major groups, namely, (i) grasping and cutting, (ii) reachability and steerability, (iii) transmission, (iv) sensing, (v) implants and deployable devices. The scope and prospects of surgical devices using CMs are also discussed.