Quests are unlocked at player level 10.It has the daily and weekly quests, as well as the Challenge Events and Seasonal Events.

Daily Quests:
Harvest Food
Mining Iron
Trade Resources
Get Experience

Rare Daily Quests:
Get Diamonds
Get Diamonds II
Find Items
Find Items II
Search for Material
Search for Material II
Acquire more trainees
Acquire more trainees II

The color Rotation Quests
The rewards for completing a rare quest are 2 heroes' ascension items.
Challenge of Chaos
Challenge of Nature
Challenge of Heaven
Challenge of Undead
Challenge of Sand
Challenge of Balance
Challenge of Balance II

Seasonal and Challenge Events
Each season brings with it 1 of 6 special Seasonal Events which also show up under the Quests button. These are:
Anniversary carnival
Winter Challenge
Romantic time
Easter Egg Treasure Hunt
Midsummer Night Carnival
Black Sail

Challenge Events
Hercules' Trial
Excalibur
Dragon Slayer
Regal Banquet
The magic lamp