There are two types of quests in Core: reward quests and reward points games. To view active quests you must go to the main menu and either press the Earn Rewards button or click on the icon for Reward Points itself.
Reward quests act like daily challenges in other games. They are started automatically and will ask players to do certain things such as playing one game in the active games list or enter three different portals in Core World. They may also ask players to participate in a game that falls under a specific category of game. After you click on a game it will display which category the game falls under. Upon completing these quests a notification will pop up and award the player the points.
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Reward points games require you to log in to certain games from the Core World. In these games the player is required to complete certain challenges. This can vary from playing the game a certain amount of time or completing an objective. Once they have done so, a notification will pop up and award the player their points. For reward points games, there is a daily cap that changes and will limit how many points they can earn.