Dark Bishops are Hexen's equivalent of the Disciples of D'Sparil from Heretic: flying, spellcasting humanoids enshrouded by robes. Dark Bishops don't handle as much damage as the Disciples do, with 130 Hit Points, and their projectiles do less damage at 4 Hit Points per projectile and 12 projectiles fired per attack. As such they are somewhat less of a threat than the Disciples are (which is counteracted by there being more of them). Dark Bishops can, however, move around fast, leaving afterimages of themselves behind, and they fire homing projectiles that move in a spiral pattern. Dark Bishops also have a close range attack which does the total damage from a stream of projectiles in one hit. However, they cannot use it unless you are directly adjacent.
When a Dark Bishop is killed, it explodes like a bomb and will hurt the player if they are too close to the explosion radius. They are apparently aware of this, as they will often try to deliberately move close to the player if they are taking a fatal amount of damage. This explosion also hurts monsters, so it can be used to the player's advantage. But if the Mage freezes them with frost shards, they will turn into an ice statue and then disintegrate harmlessly like anything else. Like Afrits, Dark Bishops are sometimes contained within destructible objects, usually, but not always, suits of armor (strangely, in the Heresiarch's Seminary, there is one hidden in a tiny pot).
They first appear in the third hub, Heresiarch's Seminary.
If you are the Mage and you use an Icon of the Defender, their projectiles will not only be reflected but will home in on the Dark Bishops instead. However, the projectiles will veer away from you until the Icon runs out, although the bishops keep attacking.
One of the ambient phrases spoken by the Dark Bishop, when played backwards, seems to be "dark bishop."