The ability of a system to correctly respond to a sudden adverse event is critical for high-level autonomy in complex, changing, or remote environments. By assuming continuing structural knowledge about the system, classical methods of adaptive or robust control largely attempt to design control laws which enable the system to complete its original task even after an adverse event. However, catastrophic events such as physical system damage may simply render the original task impossible to complete. In that case, design of any control law that attempts to complete the task is doomed to be unsuccessful. Instead, the system should recognize the task as impossible to complete, propose an alternative that is certifiably completable given the current knowledge, and formulate a control law that drives the system to complete this new task. To do so, in this talk I will present the emergent twin frameworks of quantitative resilience and guaranteed reachability. Combining methods of optimal control, online learning, and reachability analysis, these frameworks first compute a set of temporal tasks completable by all systems consistent with the current partial knowledge, possibly within a time budget. These tasks can then be pursued by online learning and adaptation methods. The talk will consider three scenarios: actuator degradation, loss of control authority, and structural change in system dynamics, and will briefly present several applications to maritime and aerial vehicles as well as opinion dynamics. Finally, I will identify promising future directions of research, including real-time safety-assured mission planning, resilience of networks, and perception-based task assignment.