With Marvin's do dates you can schedule tasks to a specific day. This means you intend to do that task on that specific day. 

There is a separate view for each day. You can navigate to each day with the arrow keys (forward and backward arrows) or the calendar in the sidebar (if you configured your sidebar to have a calendar). 

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If you did not complete a task that was scheduled to a previous day, Marvin will

collet all left behind tasks and alert you that some tasks are "left behind"
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Clicking on the reschedule button shows you a list of all tasks that are scheduled to a day in the past. You can now process them manually.
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You can click on the checkbox to complete them if you forgot to check them off.
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You can also select all of them with the "select all" at the top or by pressing cmd+a on your keyboard.

​Bulk selection works as well here. Use the shift key to select the start and end of a selection, or use the cmd key to pick single tasks.
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You can bring up this dialog with the shortcut "r" (for rescheduling).
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By using this strategy you can have all unfinished tasks automatically moved to today.

In the settings of this strategy you can choose at which time you'd like tasks to roll over, and also if you want recurring tasks to be rolled over as well.