Booty Calls features two types of quests, accessible from the corresponding button at the bottom of the game screen. Click/tap on Quests to check them out:

1. Daily Quests - these reward you with various goodies after claiming them from the chest bar in the image below. Completing the quests listed below will grant you points for advancing the progress bar:

You may also instantly complete these daily quests by clicking the Skip button and paying the required amount of gems.

Also keep in mind that Daily quests reset at 00:00 UTC, so make sure to complete them until that time.

2. General quests - these grant you rewards for each completion, and do not expire over time.