I am about 25% through the game right now and I'm starting to notice a pattern. Whenever I kill a boss it shows Congratulations! on my screen and all of my team members posing there. The thing I don't get is that it shows no reward. Do bosses in this game have no reward other than getting past them?

IIRC, they only grant you LP and Clan Points. Same thing applies to marks.

Bosses actually give you rewards. But not straight out of the battle as monster drops. You have to go talk to Montblanc and he will give you a reward. He'll mention what boss it is about and then you get your reward.