So you assign a bunch of stuff to other people (one of the fun things about any CRM system if you can't call it "fun") but you need to show the status. There are a couple of ways, my favorite way is listed here.
Where I start is always on the home page. I can then view my calendar, my tasks, and a few dashboards. However, in the calendar area (a little used feature in my experience), you do have options to see multiple calendars, your calendar or a task list. For these purposes we're going to go the task list but feel free to explore the multiple user calendar as that's very helpful to see what your colleagues are doing today.
Once in the tasks area, you have views just like a normal object, but there's something a bit different in the view area. By default there's something called My Delegated Activities which is great.
This view is based on a particular item that's only there for views that are based on activities.
Feel free to make your own views like "My Delegated - Open" or "My Delegated - Closed" for instance, whatever works for you.
Keep in mind you could always create a report (with activities as the base object) as you do have "My Team's Activities", "My Activities", or "My Delegated Activities" as the option.