Cool-headed and rational, Koujirou Shindou is a government official and master negotiator with a well-earned reputation. While departing on a business trip, a giant cube materializes and his plane is taken undamaged into the mysterious, indestructible structure. As Japanese authorities attempt to identify the cube's properties and origins, Shindou encounters an otherworldly entity known as Yaha-kui zaShunina, who materializes in the form of a human man. He assures Shindou that the passengers are not in any danger and requests help in negotiations with the human world. Hailing from a higher dimensional universe known as Novo, Yaha-kui zaShunina is able to transfer information between Novo and Shindou's universe through a cube called Kado. Despite having these unfathomable abilities, he does not appear hostile. Instead, he announces that he has come to this world with only one intention: to advance humanity—starting with Japan.

Jesus Christ and Gautama Buddha, the founders of Christianity and Buddhism, are living together as roommates in a Tokyo apartment while taking a vacation on Earth. The comedy often involves jokes about Christianity, Buddhism, and all things related, as well as the main characters' attempts to hide their identities and understand modern society in Japan.

In the Victorian era, the British Empire is bustling with the energy of the steam-powered industrial revolution. Following in the footsteps of his famous family of inventors, James Ray Steam enjoys his youth in Manchester helping at local factories and stealing components for his own creations. One day, he receives a package containing a strange ball with an attached valve from his grandfather, who has been working in the United States alongside Ray's father. However, it is not long before people from the O'Hara Foundation storm into his house demanding he hand it over. Confused and afraid, Ray attempts to flee to the home of his grandfather's colleague, Robert Stephenson, with pursuers hot on his trail. While Ray seeks to piece together the secret of the ball and discover the power it contains, it seems practically everyone in the British Empire is ready to seize it from him.

Fifty years ago, malevolent stones known as Dark Brings brought about the Overdrive, a calamitous event that destroyed one-tenth of the world. In the present day, the nefarious organization Demon Card seeks the Dark Brings' power for their all but innocent intentions. Haru Glory, a sword-wielding silver-haired teenager, inherits the title of Rave Master: the person who wields the power of the legendary Rave Stones, artifacts capable of destroying the Dark Brings. However, the many Rave Stones were scattered across the globe as a result of the Overdrive, allowing Demon Card to continue their malpractices. Groove Adventure Rave follows Haru, his strange dog Plue, the fiery blonde Ellie, and the infamous thief Musica, as they embark on a great journey that will take them around the vast world, searching for the Rave Stones that will finally end Demon Card's injustice.