Within Teamwork, when viewing tasks in board view you can choose to archive any cards that you have marked as complete.
You can mark cards as complete by ticking the arrow next to the card title which will then turn green to indicate its complete.
Once a task is complete you can choose to archive all completed tasks on a column by clicking the downward facing arrow at the top of the column and choosing Archive completed cards.
Once you choose this the completed cards will be moved from the column to the archive.
You can view the archive by clicking the options button (three dots) in the top right and choosing View Archived Cards.
A pop-out quick view window will appear showing the archived cards. You can choose to mark them as active by selecting the green tick, or view the task details by clicking on the magnifying glass icon to the right of the task name.
You can also unarchive cards by clicking the cards in the Archived quick view. When cards are selected, you will see an Unarchive Card(s) button in the bottom right.
Unarchiving will move the cards back to the column they were previously in.
Note: Archiving cards in board view will not affect any tasks within the list view.
For more information, see: Managing Board View Columns