All the tasks usually have a deadline. In this way, people responsible for the task also know within which time period they have to finish the task as it is not necessary that one responsible have only one task to perform. There can be many tasks running in parallel. In Odoo, it is clearly visible in the Project pipe if any of the tasks has passed the deadline. The due date will appear in RED. It will be easy for the project manager to see the tasks that have passed the deadline.
Assume that there are some tasks that have already passed the deadline in the In-Progress stage. Let's create two more tasks (assuming today is August 14, 2017), where I set a separate deadline. Then, let's see how the tasks will look once the deadline is passed and how they will look in the Kanban view as well as in the list view:
Look at the preceding screenshot, it is easy to track that which tasks crossed the deadline and not finished yet, the deadline date as displayed in RED color, as a project manager you can easily track those tasks and put them high priority.