Akatsuki is a small organization by most standards; at any given point, the group has at most ten members and an uncertain number of agents. Though they seem to have a decent network of agents in various villages, these individuals are usually under some form of mind-control. A notable exception is Tobi, who acted as subordinate to Zetsu before being promoted. The members of Akatsuki are all S-class criminals, the most wanted and dangerous individuals in the Naruto universe.
The exact criteria for admission into the group are unknown, but extraordinary fighting ability and ruthlessness seem to be prerequisites. Unique traits (genetic or otherwise) also seem to be a common factor among its members. Two of the more prominent members so far, Itachi Uchiha and Sasori, both undertook some sort of challenging task at the time of their entering the group. Sasori mentions during his fight with Chiyo and Sakura Haruno that "[he] hadn't had this much difficulty since joining Akatsuki." Itachi was responsible for murdering his whole clan (save for his little brother, Sasuke) around the time he is believed to have entered, but it is not certain that the two events are linked. At least in Deidara's case, the leader seems to locate potential candidates for membership and has them forcibly recruited by the current members.