Without a driver to fall back on, a fully self-driving car needs to be able to handle any situation it can encounter. With the perspective of future safety systems, this research studies autonomous maneuvering at the tire-road friction limit. In these situations, the dynamics is highly nonlinear, and the tire-road parameters are uncertain. To gain insights into the optimal behavior of autonomous safety-critical maneuvers, they are analyzed using optimal control. Since analytical solutions of the studied optimal control problems are intractable, they are solved numerically. An optimization formulation reveals how the optimal behavior is influenced by the total amount of braking. By studying how the optimal trajectory relates to the attainable forces throughout a maneuver, it is found that maximizing the force in a certain direction is important. This is like the analytical solutions obtained for friction-limited particle models in earlier research, and it is shown to result in vehicle behavior close to the optimal also for a more complex model. Based on the insights gained from the optimal behavior, controllers for autonomous safety maneuvers are developed. These controllers are based on using acceleration-vector references obtained from friction-limited particle models. Exploiting that the individual tire forces tend to be close to their friction limits, the desired tire slip angles are determined for a given acceleration-vector reference. This results in controllers capable of operating at the limit of friction at a low computational cost and reduces the number of vehicle parameters used. For straight-line braking, ABS can intervene to reduce the braking distance without prior information about the road friction. Inspired by this, a controller that uses the available actuation according to the least friction necessary to avoid a collision is developed, resulting in autonomous collision avoidance without any estimation of the tire–road friction. Investigating time-optimal lane changes, it is found that a simple friction-limited particle model is insufficient to determine the desired acceleration vector, but including a jerk limit to account for the yaw dynamics is sufficient. To enable a tradeoff between braking and avoidance with a more general obstacle representation, the acceleration-vector reference is computed in a receding-horizon framework. The controllers developed in this thesis show great promise with low computational cost and performance not far from that obtained offline by using numerical optimization when evaluated in high-fidelity simulation.