History
Akatsuki was created for the purpose of collecting the nine tailed beasts. Both Madara Uchiha and Nagato have claimed to be the creators of the organization, the former after leaving Konohagakure, the latter some time after the Third Great Shinobi World War. Nagato is regarded as the "leader" by most of Akatsuki for as long as he is alive, though he takes orders from Madara, who replaced him as leader after his death. Regardless of who created Akatsuki, it is believed that Akatsuki was first formed in Kirigakure. Although there is no known evidence for this rumor (though Madara was apparently once a Mizukage), other villages blame Kirigakure for Akatsuki's actions.
In its early days, Akatsuki was a mercenary group for hire. In times of peace most of the ninja villages, rather than increase their own armaments, employed Akatsuki to fight in wars, spy on enemies, or carry out assassinations. The Fourth Raikage claims that only Kumogakure has never used Akatsuki's services. Eventually, Akatsuki would begin capturing the tailed beasts, in the process antagonizing many of its former clients.
Events relating to Akatsuki before the start of Part II have only been given in pieces. Sasori and Orochimaru were partners for a time and were apparently very effective. Kakuzu had a number of partners that he killed in fits of rage. For this reason he was partnered with Hidan shortly before the start of Part II, Hidan's immortality meaning there would not need to be constant replacements. Itachi Uchiha apparently joined before carrying out the Uchiha Clan Massacre for which he defected from Konoha, though his membership seems to have come with the stipulation that Akatsuki could make no direct movements against Konoha. When Itachi joined, Orochimaru attempted to steal his body in order to gain the Sharingan. This failed and he was forced to defect. Deidara was recruited to replace Orochimaru as Sasori's partner, but because Orochimaru took his Akatsuki ring with him he could not also replace Orochimaru's position. Akatsuki also captured two tailed beasts before Part II, which in the anime are indicated to have been the Five-Tails and the Seven-Tails.
Akatsuki becomes much more active in Part II. At its start they assault Sunagakure to capture the One-Tail, but Sasori is killed. Madara, disguised as "Tobi", replaces him. Next are the Two-Tails and Three-Tails, though Hidan and Kakuzu are lost during an unrelated scuffle with Konoha ninja. After obtaining the Four-Tails, Deidara dies during his fight with Sasuke Uchiha, who soon afterwards kills Itachi too. After Madara's conversation with Sasuke regarding their shared legacy of hatred as Uchihas, the latter then begins working with Akatsuki with his personal team Taka. Although Akatsuki lost five members at this point, Madara claims it was worth it in order to gain Sasuke's loyalty. Despite this, their diminished numbers forced Akatsuki to become more drastic in their efforts.
In the anime, Nagato goes to Kirigakure to capture the Six-Tails (the beast having been caught at some earlier point in the manga). He and Konan are then sent to Konoha to capture the Nine-Tails. Konoha is destroyed, but they fail in their assignment; Nagato dying and Konan leaving the organization. 
At the same time, Sasuke and his team are tasked with capturing the Eight-Tails, but they fail too complete the assignment. Akatsuki's actions finally provoke a response from the ninja villages, who hold a Kage Summit to discuss what should be done. Madara, wishing to accelerate his plans, infiltrates the meeting and declares war against the great nations, promising to use the seven tailed beasts Akatsuki has already captured as weapons. The villages and their associated countries form a Shinobi Alliance to combat Akatsuki, beginning the Fourth Great Shinobi World War.
At the same time, Sasuke and his team are tasked with capturing the Eight-Tails, but they fail too complete the assignment. Akatsuki's actions finally provoke a response from the ninja villages, who hold a Kage Summit to discuss what should be done. Madara, wishing to accelerate his plans, infiltrates the meeting and declares war against the great nations, promising to use the seven tailed beasts Akatsuki has already captured as weapons. The villages and their associated countries form a Shinobi Alliance to combat Akatsuki, beginning the Fourth Great Shinobi World War.