It's a sequel to Danganronpa: The Animation (2013) and a spin-off of the computer game franchise. It's also kind of amazing. It's not perfect, but it's shocking and it hit me pretty hard.
Firstly, I'm going to be censoring this review. Everything and everyone here is a walking spoiler for the 2013 series, since in this franchise just surviving to the final episode feels like a miracle. To get around this, I'll give all the characters false names. Secondly, we need terminology.
1. GAMES - lots of them, from 2010 onwards. Story-heavy and so dark that fans bashed Danganronpa 3 for not having a sufficiently bleak ending.
2. DTA, i.e. Danganronpa: The Animation - the 2013 anime series, in which schoolchildren play a murder game at the behest of a teddy bear called Monokuma. Wild colours and designs, extreme carnage, hugely entertaining. However it's about hope vs. despair, with the ending raising the stakes to SPOILER level.
3. TEoHPHS, i.e. The End of Hope's Peak High School - the umbrella title for all related 2016 anime. Structurally it's interesting. You see, most of the 2013 series followed a straightforward pattern. The episodes would alternate. Murder, investigation, murder, investigation, etc. TEoHPHS is doing something not dissimilar, but in a much more ambitious way than the safe "remake as sequel". It's ditching a lot of the entertainment value, instead going hard for brutality, death and despair, while splitting itself into two storylines with alternating prequel and sequel episodes. These are:
4. Future Arc (TEoHPHS episodes 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 and 23) - the sequel episodes, originally broadcast on Mondays. Watch this show in broadcast order. Time after time, one arc will be either setting up or paying off something that's happening in the other arc's equivalent episodes. If you try watching either arc on its own first without interleaving it, you'll spoil the other arc for yourself and miss all kinds of shocks and surprises. This arc stars the survivor(s) of DTA and is heading for what might potentially be the end of the world. (Well, another one. The first one was bad enough.)
5. Despair Arc (TEoHPHS episodes 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 and 22) - the prequel episodes, originally broadcast on Thursdays. The world hasn't yet ended (for the first time). Civilisation's okay. The sun is shining, schoolchildren are happy and everyone's happy at Hope's Peak High School. Hint: SPOILER's going to do something about that. Don't expect a happy ending.
6. Hope Arc (TEoHPHS episode 24: "The School of Hope and the Students of Despair") - the end.
7. OVA ("Super Danganronpa 2.5: Nagito Komaeda and the Destroyer of Worlds") - bonus episode, broadcast in January the following year. It's also quite good. Unusually for an OVA, it avoids pointlessness by finding an important niche in the gaps between the Despair and Future arcs. Watch it if you can, although you needn't worry if you can't since the televised episodes are complete and satisfying in themselves.
It's bleak. It's horrifying. It has one of the most apocalyptic villains I can remember offhand in anything, being a chirpy lovable idealist (and absolute monster) who believes that hope is predictable and that despair offers exciting chaos and infinite potential. (I'll call him/her VILLAIN.) VILLAIN is pure evil, but in a way that's riveting because their anti-morality and law/chaos dichotomy is so well developed. VILLAIN will destroy the world, as we already knew before ep.1. This is a quality most villains aren't allowed, since other stories tend to be more traditional about little details like that. I was riveted, although in hindsight I also don't think that that arc was quite working before VILLAIN showed up. There's set-up and character establishment that I don't think quite achieved what was required for the emotional payoffs in the second half and in Hope Arc. Theoretically it's there. It worked. Hope Arc hit me hard. However I think another two or three episodes and more carefully built storytelling would have made it even more powerful, establishing the characters more clearly in our minds and making its events more meaningful.
That arc's third episode basically gets forgotten, for instance, including SPOILER having murdered SPOILER. A theoretically colourful cast is mostly left two-dimensional and I occasionally had trouble telling certain characters apart. (To some extent I think that's deliberate, though. All three of the people I'm thinking of are normal people in a universe of freaks and weirdos, representing the audience in a world gone sanity-shreddingly wrong.)
DTA was all about hope vs. despair, but it was also a hoot. TEoHPHS goes beyond that. It really is all about hope vs. despair, to an extent that's capable of being a bit of a slog. The murder game almost immediately stops being about Monokuma and instead becomes friends and colleagues hunting and murdering each other. No one's forcing them. They're just doing it anyway. Similarly the show's exploring quite a few extreme hope/despair boundaries, with different characters having different attitudes to what needs to be sacrificed to eliminate one of those two conditions. Not all of those beliefs are sane, but they all have their own kind of logic and the show's exploring all this more thoroughly than I'd expected. (It's worth pointing out that hope and despair are more closely tied concepts in Japanese, with the relevant words being "kibou" and "zetsubou". It's the same "bou".)
However there are other themes in this rich, dark mix too. Despair Arc in particular has a lot to say about how damaging it is to obsess only about talent. Hope's Peak High School has been split into the talented elite and the faceless masses, not all of whom are irrelevant to the story. "Include the loner" is a thing. I was also blackly amused by this being a world where TV, games and anime can actually do what our moral majorities so often accuse them of. (Results: unspeakable.)
Horrible things happen. Of course the whole franchise is fantastical, but even I was shocked by what might either be torture or an amateur lobotomy... and there's room for disagreement about whether that's even the most horrifying thing being experienced just then by the victim.
Surprising things happen. This show can make you swear at the screen just by rolling its end credits.
Despair Arc is also more mundane visually than DTA, incidentally, while Future Arc is bleak, grey and almost colourless.
I loved it. However I'd loved DTA, so I was already primed. Watching this without having first watched DTA would be a terrible idea, partly because you'd be lost and partly because much of its power comes from the fact that it's heading for the The Biggest, Most Awful, Most Despair-Inducing Event in Human History. We know this before it starts. We've seen it. VILLAIN's going to destroy us all. I've seen some viewers criticise this series for being so dark and doomed that it's impossible to care, while others complain about the positive ending. Personally I think those justify each other. The horror means that the ending is earned, while conversely the ending makes it possible to watch this show without slitting your wrists afterwards.
(Oh, and apparently it's also a sequel to the games. I haven't played any of them and I was fine, but at one point I did find myself googling one important and hitherto game-only character.)
As I said, it's not perfect. We don't get to know the (large) cast nearly as well as in DTA and they're not all well used, which can make some of them seem expendable and one-note. It can be hard even to remember everyone's one-line character description and/or special talent. There are pacing problems. The ending is controversial. Personally, though, I'm happy to live with all that. I'm impressed by the show's tone, by how boldly it's struck out in new directions and by the ambition of what it's achieved with two interleaving storylines. Some characters are written powerfully, with memorable bonds between them. The Future Arc's killing game is innovative. VILLAIN is staggering. Also, importantly, it's just as interested in hope as in despair, with the show not being a soul-crushing downer at all for me. I found the end of TEoHPHS emotional. I loved it.