A new space race is imminent, with several industry players working towards satellite-based Internet connectivity. While satellite networks are not themselves new, these recent proposals are aimed at orders of magnitude higher bandwidth and much lower latency, with constellations planned to comprise thousands of satellites. These are not merely far future plans - the first satellite launches have already commenced, and substantial planned capacity has already been sold. It is thus critical that networking researchers engage actively with this research space, instead of missing what may be one of the most significant modern developments in networking. In our first steps in this direction, we find that this new breed of satellite networks could potentially compete with today's ISPs in many settings, and in fact offer lower latencies than present fiber infrastructure over long distances. We thus elucidate some of the unique challenges these networks present at virtually all layers, from topology design and ISP economics, to routing and congestion control.