The first human steps into outer space have been among the most spectacular and potentially consequential events in the globalization of Earth. ‘Space Expansionist’ thought makes ambitious and captivating claims about both the feasibility and the desirability of human expansion into outer space. But if arguments for space expansionism are broken down into their parts, and systematically assessed, a very different picture of the space prospect emerges. There are strong reasons to think that the consequences of the human pursuit of space expansion have been and could be very undesirable-- even catastrophic.