Stair climbing is one of the most challenging tasks for vehicles, especially when transporting people and heavy loads. Although many solutions have been proposed and demonstrated in practice, it is necessary to further improve their climbing ability and safety. This paper presents a systematic review of the scientific and engineering stair climbing literature, providing brief descriptions of the mechanism and method of operation and highlighting the advantages and disadvantages of different types of climbing platform. To quantitatively evaluate the system performance, various metrics are presented that consider allowable payload, maximum climbing speed, maximum crossable slope, transport ability and their combinations. Using these metrics, it is possible to compare vehicles with different locomotion modes and properties, allowing researchers and practitioners to gain in-depth knowledge of stair-climbing vehicles and choose the best category for transporting people and heavy loads up a flight of stairs.