Snake robots have the potential to make substantial contributions in areas such as rescue missions, firefighting, and maintenance where it may either be too narrow or too dangerous for personnel to operate. During the last 10–15 years, the published literature on snake robots has increased significantly. The purpose of this paper is to give a survey of the various mathematical models and motion patterns presented for snake robots. Both purely kinematic models and models including dynamics are investigated. Moreover, the different approaches to biologically inspired locomotion and artificially generated motion patterns for snake robots are discussed.