Full story
In August 1945, Logan is held in a POW camp near Nagasaki when the atomic bomb hits. He saves a young Japanese officer, Ichirō Yashida, by shielding him with his own body down a well. Decades later, Logan lives alone in the Yukon wilderness, haunted by dreams of Jean Grey, whom he had to kill. A young mutant named Yukio, who sees deaths before they happen, finds him and brings him to Tokyo. Yashida, now a dying tech billionaire, wants to say goodbye. He actually wants more: he offers to take Logan's healing factor and give him a mortal life, something Logan has always claimed to want. Logan says no. That night, Yashida's doctor, Dr. Green, plants something in him while he sleeps. By morning, Yashida is dead.
At the funeral, the yakuza try to kidnap Yashida's granddaughter, Mariko. Logan protects her, but notices he is bleeding and not healing. The escape includes a fight on top of a bullet train and ends at Yashida's old house in Nagasaki, where Logan and Mariko fall in love. Mariko is taken again. Logan learns her grandfather left the whole empire to her instead of to his son, Shingen, who set up the kidnapping with her fiancé, a corrupt government minister.
Yukio has a vision of Logan dying. He gets an X-ray and finds a robotic parasite on his heart, blocking his healing. Logan rips it out himself in the middle of a fight with Shingen, and kills Shingen with his claws. The trail leads to Yashida's home village, where ninjas led by Harada, Mariko's old friend, capture Logan and strap him into a machine built by Dr. Green, a mutant called Viper.
Then comes the Silver Samurai, a giant suit of armor with adamantium swords. Harada realizes he picked the wrong side and dies helping Logan. Yukio kills Viper. The Samurai slices off Logan's claws and starts draining his healing factor. Inside the armor is Yashida, who faked his death and grows younger by the second. Mariko stabs him with the severed claws, Logan's bone claws grow back, and he throws Yashida off a ledge. Logan lets go of Jean's ghost, says goodbye to Mariko, who takes over the company, and leaves with Yukio.
In the mid-credits scene, two years later, Logan walks through a US airport. Magneto appears, powers back, and warns that humans are building a weapon against mutants. Right behind him is Charles Xavier, alive. What comes next is left open.

