Quests are adventures that consist of several Waves of enemies players must defeat. Players can take on Quests in groups of up to five. By completing Quests, players can earn a variety of rewards. However, if a player retires before completing the quest, they will still keep any experience earned. Also when a player enters a quest they lose AP. If you see all the enemies required, you receive a gem.
Normal Quests contain the main story of Unison League. As players progress through Normal Quests, they'll rank up and unlock various other quests.
Event Quests are time-limited quests that offer a variety of rewards. Augment and Reforge Quests, which appear on a regular weekly schedule, offer players a chance to gather materials that can be used to improve Gear. Other Event Quests, which usually run for around two weeks, often offer players the opportunity to earn a variety of Gear.
Sub Quests contain side stories that are unlocked as players progress through the main story. Completing Sub Quests typically offers special rewards such as 
Cost Points. The special items needed to unlock Advanced Classes are also obtained through Sub Quests.
Recommended Quests will show up to 10 Normal or Sub Quests that other players are currently undertaking. The suggested quests usually match the player's current rank. If a player is not of sufficient rank to join the quest normally, it will not appear under this option.
Help Friends allows players to join their currently questing friends. When a player joins their friend's or guild member's non-event quest, the AP cost will be halved. If the friend of guild member is level 20 or lower, there is no AP cost for joining. If a player is not of sufficient rank to join the quest normally, it will not appear under this option.
Redo Last Quest is a quick link back to the last quest a player joined. Quests started via Recommended Quests or Help Friends will not count. If the last quest was time-limited and no longer available, this option will be greyed out.