Conventional medical instruments are not capable of passing through tortuous anatomy as required for natural orifice transluminal endoscopic surgery due to their rigid shaft designs. Nevertheless, developments in minimally invasive surgery are pushing medical devices to become more dexterous. Amongst devices with controllable flexibility, so-called Follow-The-Leader (FTL) devices possess motion capabilities to pass through confined spaces without interacting with anatomical structures. The goal of this literature study is to provide a comprehensive overview of medical devices with FTL motion. A scientific and patent literature search was performed in five databases (Scopus, PubMed, Web of Science, IEEExplore, Espacenet). Keywords were used to isolate FTL behavior in devices with medical applications. Ultimately, 35 unique devices were reviewed and categorized. Devices were allocated according to their design strategies to obtain the three fundamental sub-functions of FTL motion: steering, (controlling the leader/end-effector orientation), propagation, (advancing the device along a specific path), and conservation (memorizing the shape of the path taken by the device). A comparative analysis of the devices was carried out, showing the commonly used design choices for each sub-function and the different combinations. The advantages and disadvantages of the design aspects and an overview of their performance were provided. Devices that were initially assessed as ineligible were considered in a possible medical context or presented with FTL potential, broadening the classification. This review could aid in the development of a new generation of FTL devices by providing a comprehensive overview of the current solutions and stimulating the search for new ones.