Autonomous vehicle technologies offer potential to eliminate the number of traffic accidents that occur every year, not only saving numerous lives but mitigating the costly economic and social impact of automobile related accidents. The premise behind this dissertation is that autonomous cars of the near future can only achieve this ambitious goal by obtaining the capability to successfully maneuver in friction-limited situations. With automobile racing as an inspiration, this dissertation presents and experimentally validates three vital components for driving at the limits of tire friction. The first contribution is a feedback-feedforward steering algorithm that enables an autonomous vehicle to accurately follow a specified trajectory at the friction limits while preserving robust stability margins. The second contribution is a trajectory generation algorithm that leverages the computational speed of convex optimization to rapidly generate both a longitudinal speed profile and lateral curvature profile for the autonomous vehicle to follow. The final contribution is a set of iterative learning control and search algorithms that enable autonomous vehicles to drive more effectively by learning from previous driving maneuvers. These contributions enable an autonomous Audi TTS test vehicle to drive around a race circuit at a level of performance comparable to a professional human driver. The dissertation concludes with a discussion of how the algorithms presented can be translated into automotive safety systems in the near future.