The Rebellion is the first sword seen used by Dante chronologically in Devil May Cry 3, passed down to him by his father Sparda. It plays the same as the other balanced DMC swords such as the Force Edge and Alastor.
After their battle on top of the Temen-ni-gru, Vergil impales Dante with the Rebellion. Dante's blood awakens the sword (which takes on a new shape) as well as awakens Dante's demon blood, alowing him to activate his Devil Trigger for the first time. Dante descends into the demon world to stop Vergil (and Arkham to a lesser extent), pitting the Rebellion vs Yamato once again. Eventually Vergil claims the Force Edge, but Dante is victorious. Successful in avenging his earlier defeat and showing the power of the human spirit, Dante officially opens up Devil May Cry for business and retires Rebellion, choosing his father's Force Edge over it.
During the events of Devil May Cry, Dante unites the two halves of the amulet himself, transforming the Force Edge into the Sparda Sword. After the battle with Mundus, the Sparda is passed onto Trish, who still uses it today. After returning home Dante returns to the Rebellion.
Dante's tasks in Devil May Cry 4 were to take back the Yamato and Sparda on behalf of his family, close all the gates to the demon world that they had opened and defeat the Order of the Sword. He gained even more Devil Arms, but stuck with the Rebellion when taking on the Saviour until Nero defeated Sanctus.
Dante continues to use the Rebellion in Devil May Cry 2, which despite being the last game in the chronological order of the series, is the Rebellion's first appearance. It was originally created as a replacement to the Force Edge and Alastor, but later developed a story of it's own in the series as one of the three swords owned by Sparda himself.