Present Experiments:
Suigetsu:
Right after Sasuke defeated Orochimaru, he went into one of Orochimaru's many experimentation labs and broke free Suigetsu, who was reduced to nothing but water, out of a holding tube. Once freed, Suigetsu threatened to kill Sasuke, after which he later told him he wanted to join him. When Sasuke replied with complete indifference, Suigetsu backed off saying that he was just testing him. Once they left, Suigetsu had Sasuke take him to the Land of Waves, to retrieve Zabuza's sword from his grave and hoping to get all the other swords from the "Seven Swordsman's of the Mist".
After leaving the Land of Waves, the two continued north to another one of Orochimaru's bases. After finding Karin, Sasuke told Suigetsu to go release the prisoners. Before releasing them however, Suigetsu told them to spread the word that Sasuke killed Orochimaru and would bring peace to the world. As Sasuke hadn't ordered him to say these things, his motives appear to be unclear.
Once Karin was persuaded to join, they headed out to get the catalyst to Orochimaru's curse seals, Jugo. They had to fight their way through an army of people branded with the Cursed Seal to reach him, and under Sasuke's orders were told not to kill any of them. When they found Jugo, who attacked them, Suigetsu attempted to kill him. However Sasuke intervened and threatened to kill both of them if they didn't stop fighting. Once Jugo calmed down, and with some persuasion on Sasuke's part, Jugo was recruited. Afterwards Sasuke told them their mission and their new team's name; they would be known as "Snake" (Hebi), and their mission was to find Itachi Uchiha.
Jugo:
Following his defeat of Orchimaru and recruitment of Suigetsu and Karin, Sasuke Uchiha traveled to Orchimaru's North base to recruit Jugo for his immense power. Initially unwilling to join forces with Sasuke, Jugo tapped into his Cursed Seal, but was then frightened into releasing it by Sasuke's killer instinct. He then joins the newly formed Team Snake in their mission to hunt down and destroy Itachi Uchiha, Sasuke's brother. Following an encounter with Deidara of the Akatsuki, Jugo discovered a hidden base belonging to the group where Sasuke confronts a clone of Itachi, who challenged Sasuke to meet him at the Uchia Clan Stronghold. Jugo remained behind with the other members of Team Snake with Kisame Hoshigaki as Sasuke confronted Itachi. After Itachi's death and Sasuke's "education" in his brother's true past by Madara Uchiha, Jugo and the other members of Team Snake were reformed into Team Hawk.
Karin:
Little is known of Karin's past other than her status as a jailer at one of Orochimaru's bases. However, Sasuke had at some point noticed her at the time of his defection and had decided to use her in "Snake" long before he rebelled against Orochimaru. Unlike the rest of the team, Karin was indeed loyal to Orochimaru, going as far to refuse the release Orochimaru's prisoners even after his defeat.
