Reef-building corals throughout the world have an annual value of tens of billions of dollars, yet they are being degraded at an increasing rate by many anthropogenic and environmental factors. Despite this, some reefs show resilience to such extreme environmental changes. This review shows how techniques in computational modelling, genetics, and transcriptomics are being used to unravel the complexity of coral reef ecosystems, to try and understand if they can adapt to new and extreme environments. Considering the ambitious climate targets of the Paris Agreement to limit global warming to 2°C, with aspirations of even 1.5°C, questions arise on how to achieve this. Geoengineering may be necessary if other avenues fail, although global governance issues need to play a key role. Development of large and effective coral refugia and marine protected areas is necessary if we are not to lose this vital resource for us all.