He is the son of Padme Amidala and Anakin Skywalker, and brother of Princess Leia Organa. As an orphan, he was raised on the planet Tatooine for the first twenty or so years of his life, where his Uncle Owen Lars and Beru Lars tried unsuccessfully to beat out all tendancies towards the Jedi Order from him. He was told that his father had been a member of the Imperial Navy and had died the death of any normal, skilled fighter.
Yoda and Obi-Wan Kenobi had hidden his sister Leia on Alderaan where he is safe from her true father. But when the Death Star intercepts her spaceship carrying plans for the superweapon/battlestation, 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 They travel towards Alderaan, only to find that the planet has been replaced by mere rock, debris, and a huge, weaponized battle station.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 excape 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 the Dark Lord brings the strong hammer of the Empire down on the planet. But Luke excapes in the Falcon. 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.
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).