The Almighty Tallests Red and Purple are the true main antagonists of Invader Zim. They are the leaders of the Irken Empire that are chosen for their height.
In the show, they both despise Zim, a young, ambitious Irken whom they sent to the previously thought to be fake planet "Earth", only to realize that Earth was actually real. They often appear in episodes where they reluctantly check up on Zim and his "mission". They first appeared in "The Nightmare Begins."
The Red Tallest is very cunning and calculating, tricking Zim into going to Earth in the first place. The Purple Tallest is rather idiotic and slow.
They both love to eat junk food and like sending young Irkens on missions to other planets. Both are the true main villains in the series.
- It was revealed in an interview with Wally Wingert that there was going to be an episode where it was revealed that the Tallest weren't actually tall, but were smaller Irkens wearing robot suits to make them appear taller.