Quests and Challenges offer some rewards more easily than in other areas of the game.
Rewards for Quests:
- Increased bonus income for kingdoms
- Unlocking challenges in kingdoms
- Unlocking the quest giver as an Epic-rarity troop (at the end of a quest line)
- Unlocking Hero Class quest lines (at the end of a quest line, not in all kingdoms)
- Unlock Explore Mode for completing the quest line
Challenges reward useful amounts of bonus souls for first-time completion of difficulty levels.
Both quests and challenges are done in specific kingdoms, so they can be played through to find those kingdoms' respective traitstones (see list here), although Explore mode is better for doing that.