Quest goals
Quests add coins for what you were going to do anyway. The bars fill on their own as you play — claim when one is full, in your own time.
How progress counts
Any game, any settled round: it counts toward spin, stake and win quests the moment the result is in.
Gems
Certain quests also drop Gems, which are what carry you up the Phoenix Status ladder.
Fresh goals
The board swaps in new quests on its own; old targets simply make way for fresh ones.