Accel World is based off the light novel series of the same name and by the same author as Sword Art Online. It actually more similarities to the setting with SAO than you would expect. It is based in the same future as SAO, but around twenty years later as 2046 where everyone has a "neuro linker", a type of machine appendage that clasps around your neck and is basically a computer that displays stuff only to your eyes. It tells the story of a normal guy called Haru in high school who is introduced to the world of Brain Burst by a beautiful and popular girl Kuroyukihime (literally Black Snow Princess).
Brain Burst is an unauthorized virtual reality program in which it speeds up the thought process of the user. One second in the real world equals to 1000 seconds when Brain Burst is activated. It's also a virtual reality fighting game in which players duel to gain points to be able to keep effectively slowing down time (imagine the advantages you can gain such as in exams or strategic sports that require quick thinking and analysis of the situation). That's about it for a high level summary of what the anime is about. Naturally, it gets more complex.
Anyway, Accel World starts off quickly in which you're immediately thrust upon into the world and see how Haru gets himself involved in all of this. The pacing is quick and we're treated off to some great fight scenes by the end of episode 2. As if that wasn't enough, a lot of tension is present in the third and fourth episodes, with a big twist in the middle of all of that. The world created is rich with a lot of little elements that make it believable (such as how the advanced technology has affected everything that we do right now). Accel World doesn't take itself easy and will frequently show off some good fight scenes, keeping up the excitement and visual spectacle.
There isn't a true antagonist in the earlier episodes since it keeps introducing new features of Brain Burst (some of which are better than others). Learning about the mechanics of Brain Burst and how deep it is keeps you sucked in. At around the halfway mark, they've managed to introduce an antagonist which will get on your nerves. Their attitude will make you hate the character, especially when things go their way. Their abilities feel overpowered and I guess it is a good job on the writer's/author's part on making an antagonist that you hate and can't wait to see them get their just desserts.
One of the more unique things about this series is that the main character isn't a handsome guy (whether it's a popular or secluded one). It's this... fat, short and chubby male who is a complete loner and gets bullied. Of course, the loner and bullied part changes and his physical appearance doesn't stop the fact that he gets his own harem (basically). Fan service can be found from time to time but it doesn't get out of hand, just a bit cliche in how it's presented and where it arises. It gets predictable in these areas which is probably the only disappointment of the anime.
The characters also have a tendency to give big speeches which can be cringe-worthy depending if you're into that stuff or not. These are characters in their early teens, set in a futuristic world and they're constantly blabbing about "master" and self-sacrifice. The fact that some of them never get over their past mistakes and constantly making reminiscences, presenting their regrets can feel overly dragging and pathetic. You want to scream at them to get past that and get onto what they should be doing. Haru himself constantly says that he needs to protect Kuroyukihime and that he is just a pawn to her so she can do anything she wishes to him. You can't take them seriously sometimes.
While protagonists needs to have some sort of weakness to keep them believable and such that you can cheer them on in impossible times, Haru can get on your nerves when he panics and gives up far too easily when something doesn't go his way. This is ironic considering he's usually the one giving motivating speeches to other people. As you would hope, the last few episodes ramp things up a little, building upon to the finale fight, the protagonist versus the pure evil antagonist. We get to see a glimpse into what made the antagonist this way and a tease into more sinister things. I don't want to spoil it but there were some good surprises.
Even thought there shouldn't be any doubt, there were a few events in the last two episodes when you thought that they might not make it. While the betrayal can be anticipated it was still shocking and the explanation might be plausible but it doesn't excuse their behavior of pretty much half the anime. I also thought it would get into the cliche area of letting the antagonist go but thankfully that was not the case. However, I still feel that the antagonist didn't get the fate that he deserved and was let off too easily.
A side effect of the anime only adapting part of the source material (four novels out of the ten released at the start of the broadcast) is that it hints at all these subplots and future arcs but we never get to see the fruits of all this setting up. One can only hope that they make the next few novels into a second season (or you can just read the light novel themselves but it's not the same). The anime has 24 episodes but there are two OVAs (Original Video Animation) that came with the games released (too bad they were never localized for the Western world), which further continue the story. These OVAs are adaptations of other events that happened from the light novels. Each OVA has a self-contained story and they are decent.
Some of the avatar designs are wicked and awesome, especially Black Lotus, who looks sleek, evil and powerful. It was actually one of the best designs I have seen in a while, love at first sight and a great blend of plated armor and mecha. There were some interesting elements in other designs such as equippable enhancements and hidden secrets. Accel World is a solid anime series that's exciting and has a decent story. While some of the characters exhibit the tiresome same old personality traits that we've all seen before, they're likable and you can't help but cheer them on. Some of the characters such as Black Lotus oozes cool and charm. Accel World is enjoyable, fast paced and features the most important aspect of a piece of entertainment: you don't want it to end.
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While I haven't watched too many anime, you can find some reviews of the animes I have watched here.