As an alternative to traditional wheeled and tracked ground vehicles, biologically-inspired legged systems are becoming increasingly common. On a macroscopic level, locomotion on land can be understood through the introduction of archetypical reductive models, capable of capturing the salient characteristics of the task-level behavior, e.g., walking or running. Unfortunately, these reductive models provide no information of the control mechanisms, through which the multiple joints and limbs of the high-degree-of-freedom-plant are coordinated to produce the observed behavior. The coordinated recruitment of the plant into a low-degree-of-freedom target model constitutes the central problem addressed in this dissertation, which aims at offering a mathematically precise feedback control solution to this problem for the particular setting of monopedal robot running. The robotic monopod Thumper, recently constructed in a collaborative effort between the University of Michigan and Carnegie Mellon University, offers a unique platform for exploring advanced feedback control strategies for running on compliant monopedal robots. The control law proposed for Thumper grows out of rigorous nonlinear controller synthesis ideas, and it coordinates the actuated degrees of freedom of the robot so that a lower-dimensional hybrid subsystem, i.e., a reductive model that encodes running, emerges from the closed-loop dynamics. This subsystem effectively governs the behavior of the robot.