This paper presents a literature survey documenting the evolution of continuum robots over the past two decades (1999–present). Attention is paid to bioinspired soft robots with respect to the following three design parameters: structure, materials, and actuation. Using this three-faced prism, we identify the uniqueness and novelty of robots that have hitherto not been publicly disclosed. The motivation for this study comes from the fact that continuum soft robots can make inroads in industrial manufacturing, and their adoption will be accelerated if their key advantages over counterparts with rigid links are clear. Four different taxonomies of continuum robots are included in this study, enabling researchers to quickly identify robots of relevance to their studies. The kinematics and dynamics of these robots are not covered, nor is their application in surgical manipulation.