SUMMARYInspired by the agility of animal and human locomotion, the number of researchers studying and developing legged robots has been increasing at a rapid rate over the last few decades. In comparison to multilegged robots, single-legged robots have only one type of locomotion gait, i.e., hopping, which represents a highly nonlinear dynamical behavior consisting of alternating flight and stance phases. Hopping motion has to be dynamically stabilized and presents challenging control problems. A large fraction of studies on legged robots has focused on modeling and control of single-legged hopping machines. In this paper, we present a comprehensive review of developments in the field of single-legged hopping robots. We have attempted to cover development of prototype models as well as theoretical models of such hopping systems.