Irken society was very hierarchical before Almighty Tallest ZIM ascended the throne. 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 were usually quite short. The Irken Republic is ultimately ruled by the Tallest and his Empress. Although Irken society seemed to be highly regimented in the past, it is 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 blood-sport matches, similar to the gladiators and warriors of ancient Rome.
Day-to-day operations of the Irken Republic are dictated by the Almighty Tallest - who are the tallest Irkens alive and thus are chosen to lead the Irken race. Usually there is only one Tallest, but if two Irkens are found to be equally tall, then they both rule together. An off-worlder can also be chosen to be the consort of an Almighty Tallest.
In the past, shorter Irkens were usually forced to work as Service Drones, and were paid as little as five monies every two years. Service Drone Bob was forced to fetch the Tallest drinks, and had to wear a table on his head. However, even though Zim was called short by the Almighty Tallest, he is not actually much shorter than the other Invaders, and is a bit taller than his current advisor Skoodge.
It is theorized that, as the Irkens are a warlike race, they were once ruled by warlords with the support of the strongest soldiers. The Tallest in the former Irken culture might be the Control Brains' adaption of this hierarchal system.
When a Tallest is killed or incapacitated, the Control Brain will choose the next tallest Irken to take his, her or their place.