If you are using the "Make a Reservation" or "Suggest an Event" Self-Book templates on your calendar, you normally have to go to the "Review Bookings" panel to see who has made bookings to your calendar. You also have to go to Review Bookings if you want to make any changes to bookings that have been made to your calendar. 

If you click on any "Make a Reservation" or "Suggest an Event" bookings in your calendar only the Event Editor will show up and not the booking details. See the image below:

As you can see you can't make any edits to your bookings directly from the calendar.

If you don't want to have to go to "Review Bookings" screen in order to edit bookings for your event you can also turn on the "Use Self-Book forms as Preferred Entry." When you turn on this feature and click on a Self-Book event, instead of the event editor you will see the Self-Book form that your visitors submitted. You can then directly edit the booking from this dialog. See the image below:

To turn this feature on in your calendar follow the steps in the image below:

Note: If "Use Self-Book forms as Preferred Entry" is turned on in a calendar, then Drag-n-Drop is completely disabled in that calendar.