Miyu Kouzuki is an 8th-grade student whose parents leave for the United States to work for NASA and arrange for her to stay with their long-time family friend, Hōsho Saionji, a monk who lives in an old temple on a hill overlooking the town of Heiomachi. However, Hōshō leaves soon after on a year-long pilgrimage to India, leaving Miyu to stay in the same house with his son, Kanata.
Suddenly, a UFO lands in the honden of the temple. Inside is a humanoid alien baby, Ruu, and his cat-like "sitter pet", Wannyā. They arrived on Earth from their home planet, Otto, when they fall into an interplanetary wormhole (a time warp which can transport objects across several regions, planets and time planes). They cannot return to their home planet because it is too far from Earth; Wannyā asks Kanata and Miyu to allow them to stay in their house, and they agree. Miyu and Kanata learn from Wannyā that people from Planet Otto look identical to human beings, and that Wannyā can also transform into human beings, animals and objects.
Miyu and Kanata feel deep love for Baby Ruu, who also cares for them – thinking of them as his parents due to their similar looks – and they go to great lengths to help and protect him and Wannya. As the story progresses the group are often involved in comedic and funny situations, but their sense of family deepens. Kanata will soon realise that he is in love with Miyu but finds it hard to confess same as Miyu. The story ends with a rescue team from outer space coming to Earth and returning Ruu and Wannyā to Otto safely. Miyu goes to boarding school alone. However, 6 years later Miyu and Kanata reunite, marry and have a daughter named Miu; they also reunite with Wannya and Ruu.
In Shin Daa! Daa! Daa!, set many years later, Ruu meets a confused earthling girl called Miu that has arrived through a wormhole. Miu desperately wants to go home and he agrees. Unbeknownst to him, Miu is the daughter of the same people who lovingly cared for him during his stay on Earth, Miyu Kōzuki and Kanata Saionji. They meet Ran, Ruu's best friend, a robot named Ann and Mininyā, Wannyā's son.