Note: Task Lists cannot be marked as complete.  Only individual tasks can be marked as complete or have dates associated with them.

When a task has been finished, click the checkbox to mark it as complete.  When a task is marked as complete, the action is noted within the task as an event.  Users can also uncheck the checkbox to mark the task as incomplete, and that will also be noted as a separate event.  The history of a task cannot be modified, and so you can use tasks to keep tabs on when certain items were completed.

Depending on how the filters are set on the left, completed tasks may not be shown immediately.  Click the "Show Completed Tasks" checkbox to see completed tasks in all task lists.  If "Show Incompleted Tasks" and "Show Completed Tasks" are unchecked, then no tasks will be shown.   When you click on a task in a task list, the complete information of the task is shown, including all activity that has been done on the task: