Your current tasks are displayed on the task panel at the left side of the screen. There are 2 types of tasks in the game:
1). Standart tasks/quests: these are tasks that follow the game plot. When you complete them, you get the new one. There is no time limit to complete these quests.
2). Timed tasks/quests: these tasks/quests have an icon and a timer - the task expires after a certain period of time. In case you complete the quest in time, you can get the unique reward what can`t be bought in the Market.