For the last four decades or so, the use of soft cable-driven surgical robots for surgery has excited the scientific world and has elicited breakthroughs in all domains pertaining to it. However, these robots are not being used extensively in all types of surgeries. To better understand the research gaps and limitations of all the technologies which have kept these robots away from practical applications, is explored in this paper. Here, all the relevant technologies and novelty related to the types of materials, kinematics and dynamic modelling, actuation techniques, and control scheme, available in literature are analyzed, keeping in mind the practicality and benefits of their implementation. By enabling intra-body operations without making multiple or large incisions, robotic technology can enhance surgery by augmenting precision, spatial flexibility, and dexterity. Furthermore, with the extensive literature survey, the areas where strong emphasis should be given are highlighted, keeping prevailing designs in mind to improve this niche technologies for unlocking of its true potential.