It's a post-apocalypse vampire story, with the survivors of humanity trying to push back against the undead in the ruins of Tokyo. It's almost addictive, but the hero's such a moron that it's tempting to see the show as a deconstruction of shounen "I've got to be the strongest!" cliches.
It's a cold war that occasionally catches fire. On the one side, we have the vampires. They treat humans as cattle, literally. They herd us together in underground communities and breed us. They'll kill children with their bare hands for amusement. They're slightly effeminate, very laid-back and entirely free of pesky morality. Despite this, though, intriguingly they also think they're the good guys. They don't think of mankind as just inferior, but as verminous and possibly evil. They probably also have evidence. They say we caused that apocalypse with a self-created virus and so far we haven't seen any better theories. When a vampire-hating character gets converted into one of them, years later he'll be just as vampire-hating as ever, but will have also become mysteriously human-hating too.
As for the free humans... well, obviously they don't like vampires. Our hero (Yuu) would feed himself to tigers if he thought it would give a vampire toothache. Their militaristic society has thus made some extreme choices, with elite vampire-hunting squads having bonded with demons to increase their fighting strength. They've done some scary research. This may or may not be connected with the monsters roaming all over the place.
The humans are actually the aggressors most of the time. They'll go on vampire-killing missions. However if the vampires decide to move, they'll do it in force and they'll bring the big guns.
The story's pretty good. It's more or less what you're imagining, but that doesn't mean it's not entertaining. It's also very marathonable and I could have happily watched lots of episodes back-to-back. However...
There's our hero Yuuichirou, aka. Yuu. He's proud. He's determined to kill vampires. He objects noisily to anything that's stopping him from killing vampires. He demands to be allowed to go outside right now and kill anything he finds, single-handedly. This is true even at the beginning, when he's a rookie with no training, no knowledge and a useless weapon. He'll later be astonished to learn that:
(a) vampires carry weapons too
(b) elite vampire-hunters carry demon-possessed superweapons and in comparison his ordinary steel sword is a child's toy
(c) there are much stronger and more knowledgeable humans than him, e.g. Lieutenant Colonel Guren, who could pound Yuu into a red smear without putting down his coffee. Even these people though literally need to be on drugs to go up against:
(d) the vampire nobles, just one of whom could kill all your squad and then wait behind you to tap you on the back before you'd finished drawing your sword. We first see one of these in action in ep.8. Holy flaming cow.
I repeat: he thought he was going to win all his fights, despite being ignorant of all that and more.
Nonetheless he never admits that he might have been wrong. The concept of losing a fight doesn't exist in his brain. This is true even when he's going to be fighting a mental battle against demons, with no experience or even any knowledge of what this will involve. His superiors are telling him he's not ready, but he doesn't care. He's going to fight that demon and he's going to win! How does he know? Don't ask complicated questions! He's the kind of cock who'll walk into a classroom of fighters and introduce himself by shouting out "I'll be taking the best weapon for myself!"
When people talk sense, he shouts them down. He hates being told to attend class when he could instead be throwing himself into combat with vampires. (His test scores are what you'd expect as a result of this.) In short, he's incredible. You'll be amazed that he remembers to breathe. He's Scrappy Doo. He's like your standard shounen hero in his obsession with being the strongest, but ten times as bad.
He gets nicer and less bone-headed halfway through the season, though. He has character growth. Note the evolution of his attitude towards making friends. Also, in fairness, I like Yuu's common-sense attitude to demon visions. He's definitely a good person, albeit not the kind of boy who'll ever change his worldview due to the evidence of reality. You'll never find anyone more loyal, although he's lucky this universe doesn't have slightly different rules on what happens to your personality when you become a vampire. I'd laugh to see Yuu in a zombie movie, for instance. ("I'll never leave anyone behind again! He's my friend!" CHOMP CHOMP CHOMP.)
It's a good show, I think. There's some extreme characterisation for both the main boys, but in both cases I can live with that. Yuu's so stupid that it feels like a feature, not a bug, while his counterpart's motivations can be really hard to fathom but I assume we're going to learn some revelations in Season 2. Presumably there are secrets we haven't learned yet. I like the world and its moral ambiguities. I like the anti-macho and pleasingly old-school vampires. It's also dark enough that apparently fandom tends to compare it with Attack on Titan, sometimes to the extent of calling it a rip-off, which I disagree with. I'm looking forward to Season 2.
"I won't lose to any demon!"