The story begins when a middle school girl named Yume sees something fall from the sky, and meets a pale violet-colored kitten named Mew. It turns out that Mew has the power of "Yume Synchro" (Dream Synchro), the power to enter dreams. In the dream world, the girl and Mew collect Dream Stones.

In the far future, the elevated irradiation from the sun has destroyed the environment of the earth and the birthrate of humans has drastically decreased. The government controls society with an army of cloned soldiers called "Ideal Children (IC)". Sam Coyne is a trader in a desert. One day, he saves a beautiful woman Maya, who has been chased by Theseus, a corps of IC. He shelters her in his trade ship, but the destroyers of Theseus surround Sam and Maya.

A seven minute epilogue to the TV series, released as an OVA.

Rudolf enjoys a life of comfort and care in Gifu, Japan. Yet true to the adage, curiosity gets the best of the kitten, and he decides to explore beyond the four walls of his home. When he's inadvertently whisked into the back of a cargo truck and lands in Tokyo, he befriends Ippaiattena, a seasoned street cat who possesses a crucial and unusual skill that will help him find his way home: the ability to read the human language. Rudolf's journey is rich with Japanese culture, and his story celebrates the wonder of discovery—that magical moment when you realize you have the key to unlock the world.