As you complete quests in game, EveryQuest will keep track of which ones you have done. It also tracks which quests you’ve failed or abandoned so that you can easily get them again. Once you complete a quest, the date and time is saved to see when you did it. Additionally if the quest is a daily quest, it keeps a running total of how many times you’ve done the quest along with the most recent completion date.

Also you can query the server for quests you’ve completed prior to your first use of EveryQuest. Access this option from the options screen