How to view an employee's employment history? / How to view employees' past promotions?

You are able to view the history and any updates of an employee's employment history in the employment info tab on their profile. You can navigate to their profile either by:

Searching for their profile in the search bar
Searching for their profile in the people's module (found in the navigation bar on the left hand side)

Clicking on one of the employment updates allows you to see more detail including the change list which tells you all of the changes made in the update.