Continuum robots are not composed of discrete joints or rigid links and thus differ substantially from conventional robots. Their structure is inspired by nature, in particular by the animal kingdom, e.g. elephant trunks, tongues, or tentacles. Continuum robots are composed of flexible, elastic, or soft materials such that they can exhibit complex bending motions. The high scalability and miniaturisation potential allow for numerous macro- and micro-scale applications, such as dexterous manipulation in constrained environments (e.g. minimally invasive surgery through natural orifices) or maneuvering in tortuous spaces (e.g. aircraft engines). The research area of continuum robots is relatively novel. While first contributions were made in the late 1960s and significant progress had been made since the 1990s in terms of efficient modelling, continuum robotics research has become an integral part of the robotics community since the beginning of this century.