This paper presents the current state of the art in mobile robots used on power transmission lines. Many theoretical and experimental studies have been conducted in order to develop autonomous machines to travel along transmission lines to perform inspection and/or repair work. These machines can improve efficiency, reduce labour costs and are expected to reduce the risk of injury to maintenance personnel. Despite there already being a number of pieces of theoretical research and technological developments in this area, problems related to stability, ability and autonomy still exist. As such, first this paper presents the main studies already carried out and the devices generally used on power transmission lines. After the latest trends have been presented, a new idea for module robots carrying out inspections/maintenance of power transmission lines is presented. Finally, the future of mobile robots applied to power transmission lines is discussed.