I've seen it called the most hated of the Spring 2014 series among American anime fans. It's a mess. It's cramming in too much plot and it's all over the place tonally. Personally, though, I think it's great and I'd defend it against anyone.
Ten years ago, the Gastrea annihilated us. Today, in 2031, the ten per cent of mankind that survived are huddled in cities surrounded by varanium monoliths, each hundreds of metres tall. Varanium is a black metal that poisons Gastrea, much like silver and werewolves. Unfortunately, though, keeping out the infestation isn't as simple as that, since Gastrea are technically a disease rather than just a bunch of really freaky monsters. If you're infected, you'll turn into another Gastrea. There are four stages, going from Stage One (disgusting slobbering mutant the size of a truck) to Stage Four (could squash Godzilla). There are also Stage Five Gastrea, but little is known about them except the obvious, i.e. stay the hell away from them.
That's the start. The worldbuilding's quite rich, apparently, but most of it got omitted in the rush of adapting four novels into thirteen anime episodes. The main twist is that there are some humans who are technically Gastrea, but aren't infectious and have themselves under control. They're called Cursed Children and they're ten-year-old girls. They're mankind's best weapon against the Gastrea, but almost everyone hates them and they generally stay under cover for fear of being beaten, abused or worse. They also have a limited lifespan, defined by a "corrosion rate" that measures the extent to which they're still human. They're normal if they're at least fifty per cent human, apart from the red eyes and superpowers. When it drops below halfway, though, they lose control and the only way to avoid mass fatalities is to kill them.
Did I mention that this decay is irreversible? All Cursed Children will turn rabid and man-eating. It's just a matter of time.
Some Cursed Children are licenced. They're called Initiators and go around with adult partners called Promoters. A lucky Initiator (i.e. not all of them) will have a Promoter who treats her like a human being, even though the flipside of a Promoter's role is presumably to keep tabs on their Initiator and kill them if necessary. This show's heroes are Enju (Initiator) and Rentaro (Promoter).
This is dark, obviously. It's brutal, it's bloody and anyone can die. If you don't like seeing ten-year-old girls committing suicide or being shot in the head execution-style, don't watch this show. What's more, the original novels are darker. There's a bombing in the anime, for instance, which in the novels was a gang beating, raping and lynching, perpetrated by civilians whom our hero had protected. (The anime isn't anywhere near that bad, fortunately. It has no rape, especially not of ten-year-olds.) This series has strong and oft-noted similarities with Attack on Titan, although one might also suggest with Full Metal Alchemist, Gunslinger Girl, Zettai Karen Children, Elfen Lied and others. Attack on Titan's post-apocalypse world is more horrific, but Black Bullet's view of human nature could be said to be even more vile.
The show's also lots of fun.
Sometimes it's just plain awesome. Enju letting rip is a sight to behold and one of the coolest things I've seen in a while. Don't be a Gastrea near Enju when she's pissed off. She'll jump out of a helicopter in flight to get at you.
At other times, though, it's light-hearted, funny and not afraid to throw around harem anime tropes, including "loli-harem" (i.e. underage girls). Like I said, all over the place tonally. Rentaro becomes the favoured object of romantic affection of most of the show's females, regardless of age, although miraculously this isn't icky. Firstly, the show's lack of focus means that the harem angle takes a while to develop and then has to fight for screentime with a ton of other stuff. Secondly, it's understated and even innocent. The only one who's openly glomping on Rentaro is Enju and with her it's just funny. Thirdly, we're still watching Black Bullet and so you're aware that the silliness might turn at any minute to body bags.
Entire episodes are capable of being basically a laugh. The world is everything I've been calling it and more, but Enju is a sweetheart, Rentaro is fiercely loyal to her and I loved watching their adventures together.
That said, though, I've heard that Enju's one reason lots of American fans hate this series. She's been called an idealised, over-adorable Little Miss Perfect. Personally, I think that's bonkers. One of my few gripes with this series is that Enju gets sidelined more often than you'd think, as Rentaro goes off without her. Comparing her with Tina Sprout, to pick a very similar character who's nonetheless much more popular with the American fanbase, both girls have a ton of darkness in them, but the difference is that we're made witness to Tina's. Enju's was all when she was younger, so we're only told about it. She was abused to the point of being practically a wild animal, while Rentaro was nearly as bad in his desire for vengeance. Finding each other helped them rediscover their humanity. They saved each other's souls. How can you not fall for two characters like that?
In fairness, I think the show briefly mishandles Enju at one point, when she and Rentaro are struggling with the question of whether mankind is so irredemably awful that it's not worth saving. (Not trivial.) Unfortunately Enju's so kind-hearted that the anime never really made me believe that she might be considering both options. That's a quibble, though. Overall, for me Enju's this show's biggest single selling point and I don't take the harem stuff seriously partly because I see Rentaro and Enju as practically married already. It's not a sexual relationship, of course, despite Enju's regularly expressed (and one hopes uncomprehending) wishes, but they're so devoted to each other that getting between them would be like getting between a mother bear and her cub. Not advisable.
Admittedly there's another character who's being set up as Rentaro's girlfriend-to-be (and is of a legal age), but what the hell. I recommend not thinking about Rentaro one day having to kill Enju when her corrosion rate reaches the danger level, though.
The plot goes too fast. Four books in thirteen episodes is too much. It bounces the story around in a way that looks scattershot, with a stunning arc finale being followed by something completely different. It can feel as if this show is really a random selection of episodes from three or four different shows, sharing the same setting but each with its own tone and subject matter. When it's funny, it's very funny indeed. The action scenes can be glorious. The political content is biting and not trying to be subtle, e.g. a character called Ayn Rand.
I've seen criticisms of the plot logic, but none that convinced me. When a monolith falls down, presumably it's more badly corroded than expected and hence below the critical level that would be required for it to do its job. Mankind's treatment of the superpowered Cursed Children is stupid (as well as evil and horrific), but that's the whole point of the story and you can see what underpins the bigotry. Other actions (e.g. what happens to the superweapon in the first book) similarly make little sense if one assumes that mankind's sole motivation is destroying Gastrea, but in fact it's demonstrated repeatedly that people are stupid, evil, greedy, short-sighted and capable of being even more dangerous than the Gastrea.
I love this show. I can see that it's a clumsily paced show with massive tonal issues and some content that's going to put off people. At one point, there was such a jump in the story that I wondered if I'd missed an episode. I don't care. Personally I find its messiness more interesting than Attack on Titan's laser clarity, although the latter is clearly a far more dramatic and successful show. (Black Bullet's opening theme music reminds me of Attack on Titan's, incidentally. They're not exactly dodging the comparison, but it would be crazy to pretend that it's trying to be that other show.) I'm not sure it gets around to answering all of its own questions (e.g. the tricycle?), but I think it ends well, with an interesting combination of unexpected darkness and reasons for optimism.
I love Enju. I think the show has heart, even if it also takes joy in finding new ways of soiling humanity. What we see of the political set-up is nasty and odd enough to be intriguing. I'd be afraid to go near the light novels, though.