As autonomous vehicles enter public roads, they should be capable of using all of the vehicle's performance capability, if necessary, to avoid collisions. This dissertation focuses on facilitating collision avoidance for autonomous vehicles by enabling safe vehicle operation up to the handling limits. The new control approaches first rely on a standard paradigm for autonomous vehicles that divides vehicle control into trajectory generation and trajectory tracking. A trajectory generation approach calculates emergency lane change trajectories, defined in terms of path curvature, that allows an autonomous vehicle to perform emergency lane changes up to its handling limits. Analysis also provides insights into when and to what extent a vehicle should brake and turn during an emergency lane change to maximize the number of situations in which a collision can be avoided. However, experimental results also highlight vehicle stabilization challenges associated with tracking paths defined by high rates of curvature change, which are desirable for emergency maneuvers. A link is forged between path curvature and vehicle performance, which inspires two trajectory tracking control designs. A four-wheel steering controller adds rear steering actuation to improve tracking and stabilization performance, while a two-wheel steering predictive controller incorporates future path information into current control actions. Experimental results demonstrate the advantages of each approach. However, separating vehicle control into trajectory generation and tracking is not always conducive to emergency maneuvers up to the vehicle's handling limits, where these aspects of vehicle control become tightly coupled with each other and with vehicle stabilization. An alternative paradigm is suggested that is more adept at controlling the vehicle in such scenarios. This approach integrates trajectory generation, trajectory tracking, and vehicle stabilization into one controller capable of mediating among the sometimes conflicting demands imposed by collision avoidance and stabilization. The controller can prioritize collision avoidance, above even stabilization, to minimize potential collisions. Experimental emergency lane changes and a mid-corner obstacle avoidance scenario highlight the advantages of this integrated approach to vehicle control.