Irken society is very hierarchical. There are several classes of Irkens which can usually be told apart by their physical appearance and height. For example, Navigators are usually quite tall (but not tall enough to become the Almighty Tallest) while Service Drones are usually quite short. The Irken Empire is ultimately ruled by the Irken Control Brains, which run the Smeet hatching facilities, choose new Almighty Tallest when necessary, and assign roles to each Irken by programming their PAK. Although Irken society seems to be highly regimented, it's possible for an Irken assigned to one class to be reassigned by the Control Brains to another one. There also seems to be no distinction or discrimination made based on gender in assigning roles, as there are several female Irken Invaders and at least one female Almighty Tallest.
Irkens compete in gladiatorial-style bloodsport matches, similar to the gladiators and warriors of ancient Rome. For example, in a cut scene from "The Nightmare Begins", Zim was forced to combat the Digestor, an arena beast, whilst wearing the armor typically worn by Irkens in these fighting tournaments.
Day-to-day operations of the Irken Empire are dictated by the Almighty Tallest, who are the tallest Irkens alive and thus are chosen to lead their race. Usually there is only one Tallest, but if two Irkens are found to be equally tall, then they both rule together. There appear to be some significant physiological differences between the Tallest and the average Irken: namely, their possession of only two fingers and unusually thin waists. However, the commentary on the DVDs revealed that the Tallest's thumbs are ritually chopped off upon accepting the mantle of leader. As for the waists, their unusual thinness could have been achieved by an extreme form of corsets.
Shorter Irkens are usually forced to work as Service Drones, and are paid as little as five monies every two years. Service Drone Bob is forced to fetch the Tallest's drinks, and must wear a table on his head. However, even though Zim is called short by the Almighty Tallest, he is not actually much shorter than the other Invaders, and is around the same size as Invader Skoodge.
When a Tallest is killed or incapacitated, the Control Brains will choose the next tallest Irken to take his, her, or their place.