New difficulty levels will become available according to schedule. You can view it in the game, in the current invasion interface.
The invasion will gradually gain momentum. With the arrival of new bosses, new distortions and adventure difficulty levels will be unlocked, and players will get access to improved equipment.
In group adventures (except Hespilon Temple), you can receive rare and epic equipment. In distortions and squad adventures, 1 epic item per day is guaranteed. After that, both rare and epic items may drop. Adventure cards usually contain information about the kind of equipment you can get in there.
Another place where you can get equipment is invasion adventures. When you defeat a special troop, you will receive a chest that may contain rare, epic, and even mythical items of relevant generation (if the character's rank is equal to or higher than the special troop's rank). The item type depends on the stage of the invasion. The chest can contain only the equipment pieces that are currently available in adventures. Bosses in invasion adventures may drop these chests as well.