You can view all existing tasks by clicking on the tasks icon on the right side of the navigation bar, just left of your profile name, and then clicking on View All Tasks.
A page with all of your tasks will then appear, from which you can filter by task status by going to the left side panel and clicking on Incomplete. Once a task is marked as completed, it will no longer appear in this list.
What happens after a task is marked as completed?
Completed tasks will be hidden from the default Task List view and removed from the general Task List view. However, you can pull-up completed tasks by going to the Task List View, then filtering by task status on the left side panel and clicking on Complete.
You can also click on Show Completed Tasks in a trip or contact to see completed tasks that were assigned to that trip or contact. Simply click on the gear icon next to the Tasks tab in the trip or contact, then click on Show Completed Tasks. Unchecking Show Completed Tasks will default the task view to show only incomplete tasks.