The Akatsuki is a group that works outside the policies of their villages. It consists of 10 members who were divided into teams of two. They were paired up based on their similarities or if their combination was compatible.
Disclaimer: This article will contain spoilers as it will contain detailed information about the Naruto series.
As they were childhood friends and the founding members of the Akatsuki, Nagato and Konan were a team. They got along very well too. As Nagato was the leader, Konan did whatever he instructed her, even though there were times when she disagreed with him. Nagato's real identity was hidden from the organization and only Konan knew his true form. He died in Konoha, after sacrificing himself to revive everyone in the village after it had been destroyed. Konan also dies later on, while fighting Tobi, when he came to steal Nagato's Rinnegan from his dead body.
Black and White Zetsu joined the Akatsuki way before Tobi, and they helped Tobi approach Nagato. Although they are two different individuals, the majority of the time they are seen merged into one and acting as a singular unit. They sometimes argue, but they never let the arguments hinder their duties or missions at any cost. They help transport the jinchuriki to the Akatsuki hideout to extract the Tailed Beasts from them. During the Fourth Great Shinobi War, Black Zetsu is sealed by Naruto Uzumaki while White Zetsu is killed by Sasuke Uchiha.
Orochimaru and Sasori were one of the first teams to be formed in the Akatsuki. They were very efficient and compatible, and even got along well, to the point where Orochimaru was aware of what Sasori's real body looked like beneath his cape.
Sasori was quite annoyed with Orochimaru when he started distancing himself from the Akatsuki’s activities, and started taking more interest in his own activities. This deteriorated their partnership which ultimately led to them changing their partners. Orochimaru was killed by Sasuke Uchiha while Sasori was killed by Lady Chiho and Sakura.
Itachi and Juzo also worked very well together as they had their own unique system of formations that synchronized their attacks with each other. They would use Itachi's genjutsu as an opening attack while Juzo incapacitated the opponent with his sword. Juzo was killed during the assassination of the Fourth Mizukage.
After the death of his partner, Itachi was partnered with Kisame. Their partnership was appropriate as they were both known for their notorious killing sprees. However, even though they both had conflicting personalities, they got along well. Even though Kisame was quite violent, he always followed Itachi's instructions. Not only that, he liked the Uchiha, so much so that he was quite sad when Itachi died in his battle against Sasuke. Kisame was later killed by Might Guy and his team.
Deidara replaced Orochimaru and was forced to pair up with Sasori. As they both viewed themselves as artists, they always found the other one inferior to themselves. Sasori believed that art was eternal whereas Deidara believed that art was an explosion, and was flashy. Despite their conflicting views, he did pay some respect to Sasori because he was the more experienced of the two, but was very disappointed by Sasori's death.
As Kakuzu used to kill his teammates in fits of rage, he was paired with Hidan, who was an immortal. All the other teams had at least tiny moments of cooperation among themselves, but it was quite the opposite for Hidan and Kakuzu. They both actively hated each other, as Kakuzu's obsession with money annoyed Hidan, while Kakuzu wanted to kill Hidan because of his annoying habits. Even though they hated each other, they are known as the most effective team in the Akatsuki. Hidan was buried by Shikamaru while Kakuzu was killed by Kakashi Hatake.
After the death of Sasori, Deidara was paired up with Tobi. Tobi annoys Deidara, to the point where Deidara feels like killing him. However, Deidara is unaware of Tobi's true identity and takes him on as a disciple, telling him about the ways of the world and about how to succeed in the Akatsuki. Deidara attempts suicide while trying to kill Sasuke Uchiha and dies.
A. Konan was Nagato’s most trusted advisor. She joined the Akatsuki when she was 18 years old.
A. Yes, Sasuke was a part of the Akatsuki but never officially. He did carry out a mission for them.
A. Deidara is the youngest member of the Akatsuki.