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Bipedal locomotion has attracted attention for its potential ability, superior when compared to wheeled locomotion, to overcome rough terrain. Even though numerous studies have been done with the goal of realizing this ability in practice, significant restrictions still remain. Currently, bipedal robots can only accommodate unplanned obstacles that are less than 6% of leg length and ground height variations exceeding a few centimeters must be known a priori. This dissertation is directed toward addressing these restrictions by pursuing a novel control design to allow MABEL, a new robot testbed with a compliant transmission, to accommodate unknown terrain with ground variations equaling 15% to 20% of leg length. In pursuit of this goal, first, the dynamics of MABEL are identified, and as a result, two mathematical models, one for control design and the other for controller verification, are derived. These models are used extensively in the design of a set of feedback controllers that can each accommodate a specific type of terrain variation. Next, a finite-state machine is designed that manages transitions among controllers for flat-ground walking, stepping-up, stepping-down, and a trip reflex. The design of each control mode and the transition conditions among them are conducted through a combination of constrained nonlinear optimization and heuristics based on how humans deal with obstacles. The finite-state machine is experimentally evaluated and results in MABEL (blindly) accommodating various types of platforms, including ascent of a 12.5 cm high stair, stepping-off from an 18.5 cm high platform, and walking over a platform with multiple ascending and descending steps.