Marvel Zombies is set in the alternate universe of Earth-2149, where the Marvel heroes have become ravenous undead. Thor: Black Winter teased the future invasion of Marvel Zombies into the main Marvel Universe. However, the living dead are already taking over, and they are overwhelming all of Marvel's martial artists.
The Avengers, Shang-Chi, and Iron Fist have all faced off against undead armies in recent stories, fighting for their very lives against the unliving. From the Seven Capital Cities of Heaven to the streets of London, zombies have been on the rise.
One of the most prominent examples of this is introduced in Iron Fist: Heart of the Dragon #1 by Larry Hama, David Wachter, and Neeraj Menon, in which Danny Rank (AKA Iron Fist) uses a portal to travel to Under City, one of the Seven Capital Cities of Heaven. Danny discovers the city is being attacked by "murderous undead ninjas" who have set the entire place ablaze. When he refers to them as "zombies," his companion, Fooh, corrects him, insisting that zombies are mindless, whereas these corpse shinobi clearly have the intelligence required to perform complex martial arts moves and even ride horses in cavalry formations. Danny soon finds the city's ruler, Dog Brother, fighting against the assailants. Meanwhile, more undead ninjas attack Danny's apartment, where Luke Cage is babysitting. After Danny returns and helps drive them off, the goddess Qwan Yin appears, carrying the (not reanimated) corpse of Tiger's Beautiful Daughter, the champion of another of the Seven Capital Cities of Heaven.
Despite what Fooh says about zombies, zombies need not be mindless drones. The entire Marvel Zombies Universe is comprised of sentient self-aware zombies. In fact, the Zombie Reed Richards even outsmarted the Ultimate Universe's Reed Richards. Clearly, Marvel zombies need not be just shambling thoughtless corpses whose only motive is their hunger. Considering that Iron Fist, Luke Cage, Dog Brother, and Tiger's Beautiful Daughter all fight the undead, there is a clear threat posed to martial artists--something seen in other Marvel titles.
Most of the martial artists in the current Avengers roster also fight the undead in last year's Avengers story "The Age of Khonshu" by Jason Aaron, Ed McGuinness, Javier Garron, and Francesco Mannon, though in this case, they battle against mummies. Captain America, Blade, and Black Panther all punch their way through these resurrected cadavers (as do other heroes who are less trained in close-quarters fighting).
Another example of martial artists fighting the undead can be seen in the fifth and final issue of the recent Shang-Chi miniseries by Gene Luen Yang, Dike Ruan, Philip Tan, and Sebastian Cheng, where the titular hero battles against a group of Jiangshi in downtown London. Accompanied by fellow martial arts masters Brother Sabre and Sister Dagger, the heroes are only able to stop these zombie-like Jiangshi after Shang-Chi is briefly turned into one.
Beyond the mass appeal of zombies in popular media, there is something else at work. Martial artists learn to find mind-body balance. While strategic thinking is critical, martial arts masters are not burdened by everyday thoughts but instead flowing through their moves with a harmoniously meditative grace. They master their own bodies and minds. Contrast this with zombies, mindless beings ruled by hunger--beings who have control of neither their minds nor their bodies. Even Marvel Zombies who retain their cognitive abilities lose control of the nature of their thoughts, consumed by their own hunger. They are the opposite of Zen, and therefore make perfect enemies for any martial artist.