I want to know what units are just about to level up.
If you select the unit, you can see the XP in the tiny bar at the bottom of the unit info mini-display, as circled in red.
You can get a numerical value by mousing over the bar (not displayed in the screenshot): in this case it will read "15 / 45 until level 3".
There are also medals indicating how many promotions the unit has, as circled in blue. You can mouse over the medals to see what the individual promotions are.