<p dir="ltr">The safe and reliable delivery of electricity is critical for the functioning of our modern society. However, high-impact, low-probability (HILP) catastrophic events (such as extreme weather caused by climate change, or cyber-physical attacks) pose an ever-growing threat to the power grid. At the same time, modern advancements in computational capabilities, communication infrastructure, and measurement technologies provide opportunities for new operation and control strategies that enhance the resilience of electric power systems to such HILP events. In this work, optimization-based operation and control approaches are proposed to improve resilience in two power systems applications. First, a real-time linearized-trajectory model-predictive controller (LTMPC) is developed for ensuring voltage, frequency, and transient (rotor angle) stability in systems engineered to operate as microgrids. Such microgrids are capable of seamlessly transitioning from grid-connected operation to an islanded mode and thus, enhance system resilience. The proposed LTMPC enables rapid deployment of such systems by reducing engineering costs and development time while maintaining stable operation. On the other hand, some power systems, such as distribution feeders, are not designed to operate as standalone microgrids. For these cases, a method is proposed for forming ad-hoc microgrids from intact sections of the damaged feeder in the aftermath of a HILP event. A feeder operating center-on-a-laptop (FOCAL) is introduced that coordinates the control of possibly hundreds of inverter-interfaced distributed energy resources (e.g., rooftop solar, battery storage) to improve system resilience. Theoretical analysis as well as numerical case studies and simulations of the proposed strategies are presented for both applications.</p>