Abstract: This research focuses on the application of existing design, modeling, and control techniques to study uninvestigated problems in the area of bipedal walking robots. The first portion of this thesis presents a method of integrating mechanism design and hybrid system analysis for the design of a class of single-degree-of-freedom (DOF) planar bipedal robots that can achieve dynamic walking gaits that are stable. These bipeds employ mechanical coordination to reduce the DOF, which can result in a reduction of the complexity of the control strategies needed to enable stable walking. Prior to this work, a methodology for the design of this type of biped had yet to be developed. The second portion of this thesis investigates walking in three-dimensions (3D). A five-DOF, 3D bipedal model is derived and is used to study the degree of dynamic coupling between frontal and sagittal plane motions. Since the dynamics are found to he inherently coupled, a feedback control algorithm that simultaneously accounts for sagittal and frontal plane motions is introduced. With this control, only unstable periodic gaits are obtained. The final portion of this thesis also involves walking in 3D but focuses on the use of a passive-dynamic walker as a basis for the development of 3D controlled bipedal models. The basin of attraction of a known, stable gait for a passive 3D biped is estimated. The stability mechanisms of the limit cycle are also analyzed. Finally, a passivity-based control strategy is introduced that results in a moderate increase in the size of the basin of attraction. Prior to this work, this methodology had yet to be applied to a 3D passive biped.