I've completed 4 missions so far, getting the upgrade unlock every time and once filling the bar at the bottom of the debriefing screen completely, but haven't gotten a single medal. What are medals awarded for? Do medals do anything?
The medals are just there as both a completionist aspect and to give the game some amount of replay value. They reflect your score upon completion of a level and are generally easier to get once you've upgraded your strike suit a bit and are further into the game. Your score is a reflection of things like the amount of time it took you to complete a level, the number of kills you have, and I believe accuracy may be a part of it as well (it's been a while since I last played).
There are 4 tiers of medals: bronze, silver, gold and platinum.
A medal is awarded when the total score bar is filled completely, if you didn't get a medal, then you fell just short of a full bar.