Every top level record type also has a STATUS drop down in the main tool bar that when changed, logs what a user changed the status from and to, and what time they changed it. You can access this history within a project from the "History" menu > "Status Changes" as shown below.
Note: Status' should change automatically based off the Action Item(s) being completed/rejected on a project if you have properly setup in the Administrator. You can find additional information on Action Items and Status' in the following section: Project Action Items