Short version: fun WWII movie with Nazi zombies. Not more than that, and is not trying to be.
Slightly longer version: JJ Abrams wanted to make a WWII movie with Nazi zombies, and by God he did just that. The important thing to understand about Overlord, though, is that Abrams wanted this to be a war movie with zombies, not a zombie movie set in a war. The actual number of zombies in the film is actually not at the level that you’d expect from a ‘pure’ zombie flick; they’re not tacked on at the end, but the film definitely builds up to the reveal and the big fight scene. This doesn’t feel like a cheat, by the way, because Overlord is also a war movie — and it turns out that the ‘parachuting behind enemy lines’ scenario is pretty damned scary, all on its own. Suspense and fear of discovery do a good job of inducing dread until the zombies show up.
The movie is also informed by a video game ethos, right down to the final cutscene — excuse me; ‘running escape sequence.’ This is not a criticism; video game conventions are no more or less appropriate for adaptation into cinema as literary conventions are. But there’s a reason why every review seems to reference Call of Duty WW2: Nazi Zombies (yes, that’s an official co-op mission); the aesthetic will appeal to those players. Although bear in mind I don’t have that game, and I liked Overlord just fine.
Bottom line is: don’t expect it to be deep cinema — and, for God’s sake, don’t overthink it; I mention that because a lot of critics seemed determined to — and you’ll have a good time. It’s gory, mind you. The Nazis are not nuanced. So the R rating is well-deserved; don’t take your kids to see it unless they’re legitimately into the entire zombie thing and can handle it. But if you can handle horror flicks Overlord does a nice job combining one with a decent WWII movie. Matinee it, at the very least.