The Exarchs are tyrannical Atlantean mages who ascended to the Supernal Realms by climbing the Celestial Ladder, which they then destroyed. Their ascension granted them godlike power, but the destruction of the Ladder wreaked enormous damage, allowing the Abyss to separate the Supernal Realms from the Fallen World and preventing most mortals from Awakening.
The Exarchs supposedly hold a great deal of sway over the Fallen World, largely through the Seers of the Throne, who believe they are servants of the Exarchs. One of their major goals is blocking access to the Supernal Realms, in order to gain exclusive power over them. However, the more influence an Exarch's given Ministry holds over the Fallen World, the more power said Exarch has. The collective of the Exarchs manifests as Supernal symbols of oppression and inequality that, combined with the Abyss, are the fundament for the Lie. Where an Exarch has placed direct attention, High Speech runes scrawl themselves everywhere, describing their wishes and goals for the area, hence the term Iron Seal for the eleven Exarchs that govern the Arcana and Abyss. Decoding these runes causes a mage to come to the attention of an Exarch, forming a dark iron door in their minds that lead to pocket realities where the Tyrants reign supreme; continuing to pry into the business of the Exarchs (such as by invoking Patron Yantras that draw on their power while not being a Prelate) will result in the mage being dragged through that door by the Exarchs' supernal servants to convert to their service or die. Seers are known to do this deliberately, as the Exarchs often reward submission with teaching Prelacies.
At any given time, there are four Exarchs that hold the title of Archigenitor. These Exarchs have the ability to bless their ministries with legacy-like powers that ignore the influence of the Lie, making them all the more powerful. But Archigenitors come and go depending on the events of the Fallen World, which makes the battle for supremacy all the more bloodthirsty among the Ministries.
Below the Archigenitors and the Iron Seals that represent the Arcana, the Seers of the Throne populate choruses and legions of lesser Exarchs. They speak of 8 million recorded gods, seven legions of Arch-Ascended under every Seal, ruling 77 ochemata and 777 secret masters of the world, and even universes within each Exarch’s soul, huge enough to spawn infinite avatars.