Citadels
Monster citadels sit on the Kingdom map. Each one holds several types of monster behind walls.

Master Coins are what unique and tournament equipment is made with.
Levels 20, 25
A Dragon Key is what opens a rare crypt, which is where the gems come from.
Levels 10, 15, 20, 25, 30Marching on one
Those walls work like the walls of a player's city, so a march with no catapults may not get through at all.
You cannot send reinforcements to a citadel. That is the sharp difference from heroic monsters, where you can.
The Watchtower tells you which of the two rewards a citadel holds before you march on it.
What both of them pay
Whichever kind it is, a citadel pays Valor, Experience and a Clan Chest on top of its own reward.
The Clan Chest goes with the citadel's level: the higher the citadel, the better the chest.
What a citadel never drops is the Armor Fragments the Triumphal Challenge asks for.
Who to send
Citadels are one of the few places the narrow captains earn their keep.
Beowulf →Brunhild →Ingrid →Ramses II →Sophia →Wu Zetian →
Bring catapults whoever leads: the walls stop a march that has none.
Working out an attack
Working out a citadel attack by hand is fiddly, so the wiki has a calculator for it.
Pick the citadel and its level, mark the troops you have and enter their bonuses. It plays the fight out and gives you the march: without losses when your bonuses allow it, and otherwise with a single stack taking every blow. It also shows the battle report it expects, strike by strike.