After the events of X-Men: The Last Stand, Wolverine, mourning the death of Jean Grey, is in seclusion in the northern wilderness. He has nightmares in which she talks to him. When some local hunters shoot a bear with a poison arrow and leave it to suffer he tracks them to a local bar and deals out some justice. This is when he meets Yukio, a strange Japanese girl, who tells him that her grandfather wants him to come to Japan because he's on his deathbed. In a flashback we see that he saved this man's life in World War II, when Logan was a prisoner of war and a nuclear bomb exploded.
He goes to Japan and the old man, Yashida, tells him that he can make him a mortal--that he can have a normal life. But Yashida dies from the cancer--and his family is attacked. In the fighting, Logan is sprayed with venom from a lizard-like mutant woman, Viper and his healing powers slow way down. Things are further complicated when he takes it upon himself to protect Yashida's other grand daughter, Mariko, who he falls in love with. She's the heir to her father's business and the assassins are after her. There's a battle at the end where Logan fights the Silver Samurai.
This is a better movie than Wolverine: Origins and sets up the situation for the upcoming X-Men movie. Recommended.