Space tourism has become a reality and is bound to become ever more affordable. It is now time to spend serious thought on how humanity is going to manage the human material culture and heritage sites on the surface of the Moon. After all, the Apollo XI mission is of global human significance inasmuch as it was the first time a human being set foot on another celestial body. Environmental conditions on the Moon are such that what is considered low-impact visitation on Earth would have devastating consequences for the heritage on the lunar surface. This paper highlights a range of issues, not the least of these being management in an environment without territorial control, neither physically nor legally. The multinational management of Antarctica is proposed as a model for the lunar surface.