Robot manipulators are increasingly used in minimally invasive surgery (MIS). They are required to have small size, wide workspace, adequate dexterity and payload ability when operating in confined surgical cavity. Snake-like flexible manipulators are well suited to these applications. However, conventional fully actuated snake-like flexible manipulators are difficult to miniaturize and even after miniaturization the payload is very limited. The alternative is to use underactuated snake-like flexible manipulators. Three prevailing designs are tendon-driven continuum manipulators (TCM), tendon-driven serpentine manipulators (TSM) and concentric tube manipulators (CTM). In this paper, the three designs are compared at the mechanism level from the kinematics point of view. The workspace and distal end dexterity are compared for TCM, TSM and CTM with one, two and three sections, respectively. Other aspects of these designs are also discussed, including sweeping motion, scaling, force sensing, stiffness control, etc. From the results, the tendon-driven designs and concentric tube design complement each other in terms of their workspace, which is influenced by the number of sections as well as the length distribution among sections. The tendon-driven designs entail better distal end dexterity while generate larger sweeping motion in positions close to the shaft.