*SPOILER*
That depends on which episode you are talking about, but some memorable doings are as follows:
In A New Hope:
Becomes the Apprentice of Obi-Wan Kenobi
Saving Princess Leia
Blowing up the first Death Star
In The Empire Strikes Back:
Getting kidnapped by a Wampa and almost dying
Fighting in the battle of hoth
Going to Dagobah to learn to be a Jedi
Fights with Darth Vader, his father, and loses his hand
Helps Leia and Han on the fourth moon of Endor
Gets kidnapped by Ewoks
Redeem his father back to the good side
In Legends (The alternate universe!):
Briefly fell to the dark side but came back, thanks to Leia
Freed Mara Jade from being evil, then married her
Started The New Jedi Order and became its first Grand Master
Had a kid named Ben Skywalker with Mara and named him after Obi-Wan Kenobi
Taught his nephews and niece the way of the Force
Went into exile after his nephew, Jacen Solo, dies
No. Luke Skywalker is a fictional character.
Luke Skywalker's paternal grandparents are Shmi Skywalker and Cliegg Lars. Shmi Skywalker was Anakin Skywalker's mother, while Cliegg Lars was the husband of Shmi and the step-grandfather of Luke.
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Luke Skywalker
luke skywalker
Luke Skywalker
Luke Skywalker :)
Luke Skywalker
Luke Skywalker.
Cade is Luke's grandson.
Definitely Luke Skywalker
Luke Skywalker