The Internet has played a key role in helping us deal with the coronavirus pandemic, a hard-to-predict rare event that significantly altered the course of our lives. However, Internet researchers and operators are mostly blind to another low-probability, high-impact event that poses a direct threat to the Internet infrastructure. In this talk, I will discuss the cosmic phenomenon of solar superstorms, which can potentially cause large-scale Internet outages covering the entire globe and lasting several months. I will present the challenges posed by this natural disaster and the preliminary analysis on the robustness of the current Internet infrastructure against this threat. Finally, I will discuss currently available mitigation techniques and lay out steps to improve the Internet’s resiliency.