Disclaimer: I'm going to try and keep this review spoiler free, but there may be minor spoilers.

With the upcoming anime adaptation and a lack of reviews on this gem of a manga, I figured I'd write one. I think that Undead Unluck is genuinely one of the best Shonen Jump series of the last couple years, so I hope that my review gets some more people to give it a shot.

First things first. The first couple of chapters are not good, and portray one of the main characters in a way that makes light of sexual assault. It's horrendous and I think the mangaka realized it, since that element is completely gone by the time the first real arc starts. Afterwards, the series gets better every arc. I don't want to sound like one of those "it gets good 10 volumes in!" people, but Undead Unluck picks up significantly around volume 4 and gets really good around volume 6. Something to keep in mind.

Undead Unluck follows Andy, an immortal who wishes to die, and Fuuko, who brings bad luck to anyone she touches, ranging from mild annoyances to death. Andy believes that Fuuko is the key to finally laying him to rest, and the two of them soon find themselves tangled up with a mysterious organization that's attempting to prevent Ragnarok.

Andy and Fuuko, first off, are great characters. After volume 1, the author tosses some less savory aspects of their relationship, and both of them continually grow as characters, which I appreciate. Andy is goofy, and wild, and full of life, but especially as the series goes on he does have a mature side that comes with his age. The mangaka has done an excellent job weaving that maturity into him while still keeping him wild, and it makes him feel very well-rounded. Fuuko starts off as you'd expect someone thrown into all kinds of craziness to, if a tad optimistic, but over time grows into a mature character in her own right.
The side characters in Undead Unluck are also excellent. For a battle shonen cast, they're unexpectedly fleshed out, and especially in recent chapters more and more insight into the side cast has been added. They have their own views and motives, and aren't all perfect, happy people like in some shonen. I can't go into much detail without spoilers, but when UU has backstories, they're well timed and normally reveal a lot about the character. Overall, could some of the minor characters be a tiny bit better- sure, but Undead Unluck has done an extremely good job with them overall. In addition, Undead Unluck has a good female cast! Some shonen seem to have issues just making the female characters people instead of tokens, but Undead Unluck avoids that pitfall.
*Updating this review a year later: Undead Unluck has continued to flesh out and even recontextualize its cast even as we approach the endgame, and it's truly incredible. I don't agree with every decision made on the characterization, but I don't need to, since they wind up being great in other ways I didn't expect. Wicked sick!

As a battle shonen, Undead Unluck has taken a lot of the typical battle shonen things- power system, power reveals, new abilities, etc- and done a great job with them. The power system is really good at tying a character's ability into their backstory and provides a lot of unique powers- you still have some typical ones like super speed and invisibility, but a lot of them are creative. I also really enjoyed how power-ups and battles were really dictated by creativity in using powers, rather than the power itself becoming notably stronger. The battles themselves are really fun, again because the powers are creative. The villains are also generally interesting, and aren't just punching bags.

As far as the story goes, the first couple of volumes are a pretty typical and fun battle shonen, but as the story goes on, it becomes more unique. Continually building upon the main narrative, Undead Unluck doesn't bring stuff into the story only to toss it, and it doesn't really go off on tangents. It just keeps bringing new pieces into the story, and it does an exceptional job weaving it all together. Tropes that are often present in battle shonen are also used well- UU doesn't subvert expectations entirely, but it plays around with tropes in ways that feel relatively fresh and clever. The series is also not afraid to take risks and go in unhappy directions, and that's especially obvious in the current arc as I'm writing this. As a side note, the current arc is absolutely incredible and has been tossing out great chapters that build the world and characters almost every week for months.
*Update a year later: even early elements that seem unimportant have been tied back into the story neatly! Little anecdotes about side cast members, explanations of the power system, they're all being used really cleverly to make the final stretch satisfying.

Art-wise, Undead Unluck isn't anything crazy, but it's solid enough and has some great moments- especially in creating striking character designs that are still reasonable. The art improves massively after the first few chapters (which look almost as though they weren't inked), and I think it fits the story well. It's rough, but has a decent bit of detail, and just like the story has gotten better as time goes on.

Overall, Undead Unluck is one of the best battle shonen I've read. It isn't perfect, but with great characters, an interesting power system, and great fights, as well as a story that just keeps on improving, I highly recommend it to any manga fan.