Until 2019, there were fewer than 200 artificial satellites in low-earth orbit (LEO) visible to the naked eye. By 2021, there will be about 2000, with tens of thousands more planned for launch in the next few years by numerous commercial satellite companies. Astronomers are used to the nuisance of an occasional satellite trailing across an image or spectrum. But the advent of “mega-constellations” of LEO satellites poses serious new challenges to our ability to carry out ground-based astronomical research. Deep wide-field imaging surveys, time-domain investigations, and projects that depend on twilight observations are especially vulnerable. And the appearance of the natural night sky itself may be changed dramatically. I will review the various satellite constellations now being launched into orbit or planned for the near future; summarize observations of their brightness as seen from ground; discuss some of their most troubling likely impacts on ground-based optical/infra-red astronomical research; describe ongoing efforts to understand and mitigate those impacts; and summarize the relevant laws and regulations governing satellites. There is an urgent need for international conversation and agreement among the many stakeholders in order to minimize the impacts of future large constellations of LEO satellites on ground-based astronomy.