One may find Outer domains as well as Underground domains called Barracks in the Alvilág.

Outer domains can be found both during exploration of the kingdom and exploration of the Alvilág and will be seen on both cells.

Barracks can be found only during the exploration of the Alvilág.

To send explorers to the Alvilág, open your Expeditionary Corps and check Alvilág next to the coordinates of the cell

Missions cannot be sent from other cities. Underground missions can be sent only from Pits, Mines, and Capitals.

That is why when trying to send a mission to the Alvilág from an inappropriate estate, you will see a notification window:

There's a penalty on the duration of all underground missions in the Alvilág: +25%.

Penalty "+25%" can be temporarily canceled with the help of a Tournament service