Oxygen is the third most abundant element in the universe (after hydrogen and helium) and of course it is important: all known life forms require liquid water and its oxygen content. For over thirty years, astronomers have been searching for molecular oxygen, O2, as part of an accounting of cosmic oxygen atoms. Despite early predictions that O2 should be abundant in the molecular clouds that form new stars and planetary systems, it is virtually absent. Only two locations have convincing O2 detections, a region of shocks near the Orion Nebula, and a cloud in the constellation of Ophiuchus. The theory is clearly wrong. What is not clear is whether O2 is missing (with dramatic implications for its abundance and the chemistry of molecular clouds), is in some less detectable form (perhaps frozen onto dust grains), or has been taken up to form water, carbon monoxide, or other oxygen-bearing molecules.