Autonomous vehicles have the potential to eliminate the vast number of motor-vehicle accidents that occur each year. However, as the burgeoning technology becomes more publicly available, self-driving cars will continue to encounter emergency situations. To maximize the vehicle's ability to navigate these situations safely, autonomous driving technology needs to be able to use all of the vehicle's performance capability. Race car drivers can inspire autonomous systems with full authority over a vehicle's capabilities because they routinely drive at or near the limits of handling without losing control. This dissertation aims to advance the understanding of how highly skilled human drivers operate vehicles at the limits by analyzing their trajectories, steering behavior, and stability characteristics observed while maximizing vehicle performance. First, a sensor suite and related methods are used to acquire research-quality, multimedia data from vintage race cars during real-world race events. The resulting publicly available database not only further documents and characterizes select, historically significant automobiles, but also provides open access to vehicle dynamics data recorded while expert drivers operated at the friction limits. To investigate the extent to which highly skilled drivers follow a theoretically ideal trajectory when maximizing vehicle performance, a statistical analysis quantifies the dispersion of paths driven by professional race car drivers during live races. The method reveals that two drivers operating the same vehicle followed measurably dissimilar trajectories, yet achieved similar overall results as measured by lap time. A state-of-the-art autonomous race car, which applies racing theory in the real world, is used to explore whether the variance observed in the human driver data is a result of error, which would imply following an optimal trajectory leads to greater performance, or whether the observed variance is a consequence of purposeful behavior essential to fully utilizing a vehicle's capabilities. The autonomous race car is as fast as a skilled, proficient driver, but currently not as fast as an expert driver. Using a quasi-steady-state model as a baseline, an analysis of each driver's steering behavior shows that the human drivers purposely operate around the handling limits, including beyond the limits, while the autonomous race car's design leads to operation up to the handling limits. Furthermore, a phase portrait analysis illustrates that the human drivers consistently operate the vehicle closer to, and sometimes beyond, the boundaries separating inherently stable and unstable vehicle states, whereas the autonomous race car's trajectories always remain within the stable region. This information can help design algorithms that operate over the full range of vehicle performance, to maximize the vehicle's ability to operate not only at speed during racing maneuvers but also safely during emergency maneuvers.