The Quest Board can be found next to the mail box leftwards from the Leader's house. These quests serve as hunts for a specific monster of that can be found in the area you are currently in. The targeted monsters can be found on routes, deliveries or main quests.
Each city can have three quests available at the same time - so if three cities have been unlocked, one can accomplish nine deliveries in total until they all refresh to grant new quests. Quests are refreshed once a timer has timed out, occurring every six hours. This process can be influenced to immediately refresh by watching an advertisement or paying gems.
After killing any quantity of enemies listed in an active quest, the transition screen will show the amount required until the quest is complete. If a quest is completed, one can redeem a chest on the board or right after the quest is finished, as it will display the completed quest alongside other quest values with the option to claim. These chests contain random materials from all the cities that are already unlocked and has a chance of giving gems.
Important Note: Sometimes one can receive a quest to watch an advertisement instead of killing a number of enemies. The rewards will be identical to other quests.