Yoda and Obi-Wan Kenobi had hidden his sister Leia on Alderaan where she was safe from her true father. But when Darth Vader intercepts her spaceship carrying plans for the superweapon/battlestation, the Death Star, she sends droids R2-D2 and C-3P0 to meet Kenobi. However, on their journey the end up enslaved to Luke himself, who follows the droids to meet the Jedi.
Joining with Kenobi, they depart Tattoine on Han Solo's ship. They travel towards Alderaan, only to find that the planet has been replaced by mere rock, debris, and a huge, weaponized battle station. Taken in by tractor beams, they barely escape the Imperials after saving Princess Leia from the Death Star's detention level. Obi-Wan Kenobi, however, is not so lucky: he dies in a final battle with Darth Vader.
They travel back to the Rebel base at Yavin 4, but they are tracked by an Imperial tracking beacon. The Death Star follows and the Empire prepares to destroy the planet with the superweapon. The Alliance uses the stolen plans to the station to lead a final attack on it. Luke himself sends a proton torpedo down a weak point in the Death Star, causing a chain reaction which explodes it. Darth Vader himself is attacking Luke in a TIE Fighter when the weapon is destroyed. Han Solo uses the Falcon to send him spinning aimlessly into space. With these victories under it's belt, the Rebel Allience seeks shelter on Hoth.
Desperate to find Luke, whom he recently learned was his own son, Vader sends probe droids into thousands of planets across the galaxy in search of the Jedi hopeful. When a droid stumbles upon him on Hoth, the Dark Lord brings the strong hammer of the Empire down on the planet. But Luke escapes in his X-wing. Following advice from the spirit of Obi-wan Kenobi, he travels to Dagobah to learn the Jedi Arts under Jedi Master Yoda. But he has a vision of his friends being captured by Vader, and against the warnings of Kenobi and Yoda, he travels to Bespin to save them, only to be trapped by Vader. On Bespin he learns that Vader is his father, and loses his own hand in combat with the Dark Lord of the Sith.
Sometime later, Luke learns the truth from Yoda and the spirit form of Ben Kenobi that Vader was indeed Luke's father, Anakin, a former Jedi Knight who turned to the Dark Side of the Force. On Endor, Luke surrenders to Vader in an attempt to bring the Dark Lord back to the good side, but he ultimately becomes a prisoner of The Emperor on the half-completed second Death Star. Luke and Vader duels one another one final time, after which Luke declares himself a Jedi as his father was before him. In defiance, the Emperor unleashes Force lightning against Luke in an attempt to kill the young Jedi. Seeing his son wounded, compassion and love finally melts Vader's heart, and in an act of self-sacrifice, Anakin Skywalker re-emerges to destroy the Emperor once and for all. On the deteriorating Death Star, at the foot of Vader's shuttle, Luke removes the former Vader's mask and looks upon his father's eyes for the first and only time before Anakin becomes one with the Force. Luke and his father's body escapes the Death Star's destruction. Back on Endor, Luke cremates his father in the manner of a Jedi's funeral, and joins in the celebration of the apparent defeat of the Empire, thus Luke comes full circle both as a Jedi and as a person.
In the Star Wars books "The Expanded Universe" Luke meets Mara Jade. He falls in love with her, and eventually they wed. They have a son called Ben Skywalker (after Obi-Wan Kenobi, who used the pseudonym Ben). He resigned his commission in the New Republic's starfighter corps to pursue his Jedi studies, a decision some anti-Jedi politicians would use against him.