Additionaly in here, you can get rewards for beating Journey Bosses for the first time. You can have up to 3 daily quests at the same time and Journey Bosses quests don't count towards that limit. When you reach your limit, you simply won't receive other quests till you complete one of them.
They are completed after reaching certain milestones, and in reward they always give you Gems.
To get to the Path of Hero, you click on the button in the top-right corner, which shows you your current progress on the ongoing quest. These are the more complex quests, which will require you to read the objective more carefully.
While the Global Event is active, you get quests which yield you Event Resources. The type of quests are different on each Event, but the most common one is to defeat Event Bosses in Event Levels. You might notice some similarities with the Path of Hero quests.