I began watching this originally as a counterpoint to becoming interested in My Little Pony, because where as that is a bright and colourful cartoon with a lighthearted tone and lots of humour, this is a dark and gritty cartoon with dark tones and good old fashioned Zombie bashing.
The basic premise is as follows, whilst at school dealing with the same problems any Japanese high schoolers have, e.g. girl troubles, school and girl troubles in school, a Zombie apocalypse suddenly breaks out seemingly at the drop of a hat, forcing a group of friends (At least I think they were friends.) to band together to survive, led by Zombie-savvy Takashi (Or maybe that was his surname, I was watching the Japanese version with subtitles, it wasn't especially clear.), though the title is a misnomer as only the first few episodes actually take place inside their school, it goes to several places from there.
My initial problem with the series was that there were many random panty and boob shots, typical of an Anime for such a demographic, it's not especially amusing because it's happens during tense and serious scenes and is very inappropriate every time it does it, also the female characters all bounce like they have water balloons attached to their chests and will wiggle at the slightest movement. But this decreases in frequency as the series progresses, so it eventually is not too big an issue.
One of my favorite things about the animation is how satisfying the zombie bashing is, and this is definitely a cause of the animation because it certainly feels like the zombies are being bashed with great force, and it's not too much of a stretch to believe they were hit that hard, and thus has a great feel to it, unfortunately the characters gradually start using guns so this too lessens as the episodes go on sadly, the guns don't quite have the same impact, despite also feeling very real. I discovered that HSOTD was animated by Mad House, the same guys who did Death Note, which I'm also a big fan of, I always felt during Death Note that the skills of the animators were wasted on Death Note due to it being more about the characters and having few action sequences to make the most of. Though one thing that I wish they didn't bring from Death Note was the shaky cam animation which baffled me even then, because no matter how much they try to convince me I'm in the thick of the action, I still know it's a cartoon.
The characters aren't poorly written, and are at least distracting to watch during the breather scenes or episodes, and Takashi, the main bloke can even be thought provoking during scenes where he performs morally questionable acts to save himself from the Zombies. The others are kind of single trait characters, but as I said, can at least hold your attention.
Another problem is that so far, there are only 13 episodes, and there's not a lot of variation story-wise, I imagine this'll be fixed if there's ever a second season, if there isn't a second season, the ending will come as a disappointment because it doesn't quite have the same tone as the rest of the series and isn't the climactic, epic ending one would expect from an Anime about Zombies. Overall though, I would recommend this series if the panty-shots don't annoy you too much and you enjoy watching Zombies get bashed with sports equipment, Shaun of the Dead style. :D