Urusei Yatsura follows the chaotic life of Ataru Moroboshi, a lustful, hopelessly unlucky high school student whose ordinary problems become a planet-wide disaster when the Oni threaten to invade Earth. The aliens offer a bizarre bargain: they will withdraw only if a randomly chosen human can beat Lum, the beautiful daughter of the Oni leader, in a one-on-one game of tag. Ataru is the unlucky candidate, and he has ten days to grab Lum's horns and save everyone.
For Ataru, the challenge is less about heroism than survival. He is driven by a promise of marriage from his childhood friend Shinobu Miyake, yet even that motivation does little to balance Lum's extraterrestrial powers and his own terrible luck. He manages to catch Lum off guard, first grabbing her bikini top by mistake before eventually completing his goal, but victory only makes things worse. Lum misreads the encounter as a marriage proposal and moves in with him, turning his life into a nonstop battle of jealousy, misunderstandings, and alien mischief. The poor student keeps trying to shake off his clingy new housemate while still hoping to reconcile with his desired fiancée, and every triumph seems destined to collapse into another comedy of disasters.