Black swan events are hard-to-predict rare events that can signicantly alter the course of our lives. The Internet has played a key role in helping us deal with the coronavirus pandemic, a recent black swan event. However, Internet researchers and operators are mostly blind to another black swan event that poses a direct threat to Internet infrastructure. In this paper, we investigate the impact of solar superstorms that can potentially cause large-scale Internet outages covering the entire globe and lasting several months. We discuss the challenges posed by such activity and currently available mitigation techniques. Using real-world datasets, we analyze the robustness of the current Internet infrastructure and show that submarine cables are at greater risk of failure compared to land cables. Moreover, the US has a higher risk for disconnection compared to Asia. Finally, we lay out steps for improving the Internet’s resiliency.