Internet security and performance problems often brew invisibly. Protecting and improving the Internet’s operations requires real-time visibility into networks and their users. However, the Internet's size, ephemerality, and diverse deployment patterns challenge visibility. In this talk, I will show how building data-collecting systems that rigorously account for the Internet's complexities reveal previously unseen critical operational challenges and threats. These include the discovery of billions of often-vulnerable IPv4 services and convoluted satellite routing patterns that take detours around the world.