I would like to be aware of the status of task allocated to staff- but I am in the dark

I would like to be aware of the status of task allocated to staff- but I am in the dark

Its all very well allocating tasks to staff, but thats the last you hear about it. What would be good is if, when the staff member completes the task, we get a message: task A has been completed by staff member B. or, even better, Task C (name of task) allocated to staff D is overdue Can this be done?