The nightmare of space debris has become a reality: fragments of missiles or satellites accumulated over 60 years in orbit around Earth are multiplying exponentially. Every new debris collides with other objects, generating even more debris. Today, they are out of control and threaten rocket launches and space installations, including the International Space Station. Yet our civilization can no longer function without satellites. Engineers worldwide are competing with ingenuity to become space garbage collectors, testing their wild projects: tugs, nets, harpoons, and other jellyfish-like robots.