This dissertation is made up of several chapters, each of which is a stand-alone document. Together, these chapters are representative of my research here at Cornell, focused on non-linear control of bipedal walking robots. Controllers for bipedal walking often rely on simple models. Here I present two controllers for simplified models, both of which are designed to be robust to bounded disturbances. The first is a foot-step planner for the inverted pendulum model of walking, and the second is a trajectory tracking controller for a double-pendulum model of walking. Next, I have a chapter that talks about some of the interesting features of simulators that include contact mechanics, like those used for walking robots. One topic that comes up repeatedly when studying bipedal locomotion control is trajectory optimization. I wrote a introduction and tutorial paper on the topic, which is included here as a chapter. I also developed my own trajectory optimization algorithm, DirCol5i, which is described in a second chapter on trajectory optimization. The final thrust of my research at Cornell was developing a walking controller for the Cornell Ranger walking robot. Here I describe my methodology for controller design. This process is divided into three parts: the first is to use simulation of the robot to develop a control architecture for the robot, which can be described using a small number of parameters. These parameters are then selected using optimization, first of the simulation of Ranger, and then using experiments on the physical robot. In discussing the results, we place special emphasis on the interplay between human intuition and computer optimization for controller design.