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In a land overrun by yoma - monsters that feed upon human innards and take on the appearance and memories of their victims - humans are little more than cattle awaiting slaughter. The only opposition to the yoma is The Organization, a group led by a council of mysterious men who send out their all-female warriors (known as claymores) to do their bidding. However, The Organization is not charitable; a town must pay an exorbitant fee for their services. Likewise, many of the claymores care little for those who they protect. Clare, the lowest ranked claymore, lives only so that she may one day avenge her mentor.
Ichigo Kurosaki is an average high school boy with a not-so-average ability to see spirits - something that hadn't affected his life much until a strange woman entered his room one day. Named Kuchiki Rukia, she's a shinigami who was sent from the spirit world to destroy a hollow - a dead-soul-turned-monster; and much to her surprise, Ichigo can see her. When the hollow suddenly attacks his family, Rukia intervenes and is injured in the process, leaving Ichigo to fight it himself. But when Rukia lends him her shinigami powers - which is forbidden - he inadvertently drains them away and has no way to return them. Now, Ichigo is a full-fledged shinigami who must juggle his studies with his newfound duty of fighting hollows; but having gained his powers through forbidden means, the spirit world isn't going to leave Ichigo alone. Ichigo and Rukia must keep their situation a secret from the other shinigami, or the consequences could be dire.
Fighting, that's what brings these two together: Fights that span most of a chapter, spilling out into others and filling up a volume with violence of a badass degree. While Bleach contains a healthy dose of fancy lad's magic and Claymore on the other hand is devoid of magic overall, both still contain the roots of good, quality sword fighting, be it magic swords or just big-ass blades.
Claymore is also the more serious of the two, firmly maintaining drama over comedy but Bleach tosses it's chips in to match it with the twists and turns of it's plot and serious moments to raise the tension. Guess it doesn't help that both worlds are a world of badass on their own, where generally non-humans combat otherworldly creatures. There are exceptions but the fantasy/supernatural reign supreme.
The series Blood + and Claymore involve strong female leads that are aloof and cold up front but display tender moments in them. Each takes part in slaying the demons of the world but also have to look within themselves to control their own demons. Both have a fantasy like quality to them.
Claymore and Blood the Last Vampire each revolve around demons. The series are dark and twisted following the struggles of the main characters as they are exiled from the people around them.
Power corrupts, and absolute power corrupts absolutely. Top-ranked student Yagami Light is disenchanted with the world around him. Through a series of events, he comes into possession of the ultimate power over life and death: a supernatural "death note" which can kill nearly anyone at his whim. As Light sets off on a crusade-turned-killing-spree, investigators from a police task force try to stop the mysterious deaths - including Light's own father, a senior policeman.
Although Death Note seems mildly unrelated to Claymore, both encompass very dark themes and twisted views of death. The characters of Light (Death Note) and Claire (Claymore) have a desire to achieve their original goal, which almost blinds them to the fact of everything else. They are simply put in a struggle for survival.