"R" (Nicholas Hoult of X-Men: First Class) is a zombie who has retained some of his humanity. When a group of humans are attacked by zombies, he ends up saving Julie (Teresa Palmer) from being killed by the undead. But the reason, at first he does this, is he has killed her boyfriend. And by eating brains a zombie gets a glimmer of their victim's lives. And so he immediately fees attached to her. But these feelings eventually become his own--and as he mental state changes he begins to physically change back into a human. And this begins to affect some other zombies...
The villains here are the "Bonies", zombies who have lost all traces of their humanity and are basically walking skeletons. When they attack the human city it's up to "R" and his brethren to help fight them. Warm Bodies is one of the more unique zombie films I've seen in a while. I think this is the beginning of a new zombie sub-genre--the ZomRom.