The global effects of climate change will increase the frequency and intensity of extreme events such as heatwaves and power outages, which have consequences for buildings and their cooling systems. Buildings and their cooling systems should be designed and operated to be resilient under such events to protect occupants from potentially dangerous indoor thermal conditions. This study performed a critical review on the state-of-the-art of cooling strategies, with special attention to their performance under heatwaves and power outages. We proposed a definition of resilient cooling and described four criteria for resilience—absorptive capacity, adaptive capacity, restorative capacity, and recovery speed —and used them to qualitatively evaluate the resilience of each strategy. The literature review and qualitative analyses show that to attain resilient cooling, the four resilience criteria should be considered in the design phase of a building or during the planning of retrofits. The building and relevant cooling system characteristics should be considered simultaneously to withstand extreme events. A combination of strategies with different resilience capacities, such as a passive envelope strategy coupled with a low-energy space-cooling solution, may be needed to obtain resilient cooling. Finally, a further direction for a quantitative assessment approach has been pointed out. Peer Reviewed