House of Thule progression is set up in the same manner as it was in Underfoot. Actual progression involves only the group missions, so you can complete only those missions as long as you have someone to request them for you.
The first two tiers are open zones:
Tier 3 zones can be accessed by completing missions in Tiers 1 and 2.
Tier 4 zones can be accessed by completing missions in Tier 3.
Most zones have two group missions in them (each of which is required for the "Hero of _____" Achievements), however actual progression involves only one mission per zone.
You must be at least Level 80 to participate in House of Thule tasks and missions.
You must be at least Level 87 to request most of the T3 tasks and ALL missions.
You must be at least Level 88 to request all of the T4 tasks and missions.
Listed below here are progression tasks by zone. Bolded tasks (each of which is a group mission in an instanced zone) are required for everyone. Unbolded tasks are required only to request the group missions.
Note: The pre-requisites listed here can be done in any order (they are not progressive and can be requested at any time).
Note: The first five pre-requisites listed here can be done in any order or at the same time (they are not progressive). "The Staff Retreat" requires that you have the first five tasks done.