When battle can't be met in the open field or forests, or your enemy just refuses to leave their walls, that's when sieges come into play.
Sieges introduce several unique mechanics to battles, as well as adding a pre-battle period where each side can build siege equipement as well as hand off leadership. Siege weaponry works in various ways, some augmenting how a side does in battle, while others focus on bringing down defenses.
Besides this, sieges directly alter how battle takes place, introducing follow-up battles, as forces from either side push the defensive line farther in or out of the city, and contact points, which simulate the attacker's ability to actually get soldiers to the walls.
Worthy of note, a besieged, and encircled, settlement will have all outgoing resources (to include unit supply) stopped while all incoming trade is considered lost. Additionally, no one will be able to enter, nor will anyone be able to leave the settlement.
Siege weaponry comes in several varieties:
Battles in sieges have several new mechanics. Firstly, and likely most importantly, the first battle may not be the only battle in a siege. A siege can, if the attackers are always victorious and the besieged settlement is heavily built up, have up to 5 separate battles.
Each separate Stage of the siege has different bonuses that come into play, primarily in what benefit the defenders get to avoiding ranged fire. With exception of the last Stage of a siege, all other battles are considered "Take the Walls" battles, where seige weaponry continues to fire and move into place, and attacks storm successively smaller, but more heavily built and reinforced interior walls, fortress, and castles.
The last battle, the "Storm the Keep" battle, is purely a melee conflict, as attackers move into the castle, fortress, or citadel proper, seeking to cut down anyone who resists. No siege weaponry comes into play here, and mounted soldiers are forced to dismount in order to engage. Ranged soldiers will use melee equipment as their weapon, if they have any.
On the other side of things, defenders may always opt to sally forth from the walls, aiming to break the siege and push the attackers further out of the city. In this situation both sides fight as if it was an urban battle. Should they be victorious the sieges moves back a stage, and if it is the outermost walls, the siege is broken.
Contact points represent how many soldiers the attackers can actually attack with. Ladders provide 1 contact point each, while siege towers provide 4. Defenders depend on contact points to engage in melee as well, thought they gain an additional point from each.
Ranged soldiers are not affected by contact points, and will continue to fire on the enemy regardless.