Luke prioir to the Return of the Jedi:
Spoiler :
New Hope/Return of the Jedi
Luke Skywalker is a legendary Jedi Master of the New Jedi Order, Commander of the Rebel Alliance and Hero of the Resistance. He is the son of Jedi Knight Anakin Skywalker and senator Padme Amidala as well as the twin borther of Leia Organa, general in the forces of Resistance. He was first seen by Yoda in his vision while the Grand Master was learning the path to immortality. At his birth, him and his sister have been taken a part so they would be saved from the Galactic Empire. He was taken by Jedi Master Kenobi to Tatooine where he would live his life as farmer with his step uncle. Once he learned of his heritage, Luke became one of the most prominent figures in the war against Galactic Emperor, helping the Rebels to destroy Death Star and saving his father from the Dark Side.
Luke after the Return of the Jedi:
Spoiler :
Return of the Jedi/Force Awakens
"Do I know Luke Skywalker? Of course I know him! Well, I mean, I've never met him, but everybody knows Luke Skywalker. He defeated the Emperor, and they say he's the best star pilot in the galaxy."
After the battle of Endor, Luke reported the Rebels that both Palpatine and Vader are dead. Rebels used the death of Empire's leaders to start the New Republic similar to the previous Galactic Republic. However many former leaders of the Galactic Empire thought that the Palpatine's death is just Rebel's propaganda and continued to fight the Rebels.
"Luke, when gone am I... the last of the Jedi will you be. Luke, the Force runs strong in your family. Pass on what you have learned, Luke."
Last wish of Jedi Grand Master Yoda was for Luke to train the new generations of Jedi. Being that the remains of the Empire were still fighting the Republic, Luke had to postpone the creation of the new Jedi Order and help the Rebels by taking numerious missions. Like the one to Vetine in order to save the ancient Jedi tree.
Galactic Civil War finally ended with the battle of Jakku and signing of the peace treaty known as Galactic Concordance. Empire's military forces were moved/vanished to the Unknown Regions (Base for the Starkiller Base) while the rest of Empire were forced to live in pre-established systems. With for being gone, Luke started the restoring of the New Jedi Order. The man who helped him greatly was Lor San Tekka who witnessed the Jedi/Clone Wars and was the member of the Church of Force. Both of them were searching for the remaining Jedi Temples and Holocrons which would help Luke start the New Order.
Among the few people Luke started training was Ben Solo, the son of Leia Organa/Skywalker and Han Solo. Leia was afraid that Ben will fell to the Dark Side, and hoped Luke would be able to stop that, similar to how he saved their father. However, Ben fell to the Dark Side of the Force, influenced by the dark being known as Snoke. Snoke was afraid that the Jedis will destroy the Imperial Weapon and ordered Ben to destroy the Order. Ben joined the First Order and became the Knight of Ren, tooking the name of Kylo Ren.
"He was training a new generation of Jedi. There was no one else left to do it, so he took the burden on himself. Everything was going good, until one boy, an apprentice, turned against him and destroyed it all. Everything Luke had worked toward: gone. Luke felt responsible. He walked away from everything."
Ben masacred the Jedi Order and destroyed everything Luke has built. Jedi Master then vanished into exile with only R2D2 and Lor Tekka knowing his whereabouts. Those close to Luke believe he went into search of the First Jedi Temole, located on Ahch-To.
Througout the Galaxy, Master Skywalker became a myth and a legend.
After the destruction of Hosnian System, the Resistance thought it's a prioirty to find their long lost hero so he would once again help them to bring justice across the Galaxy. Bu completing the map pieces (One held by R2D2, other held by Tekka), Resistanc finally found out the whereabouts of Jedi Master. Rey and R2D2 arrive at Ahch-To where Rey gives Luke his father's lightsaber as the symbol of only hope Galaxy has been left with.
Luke's Force and Lightsaber Skills - Canon
Spoiler :
It was hinted by Vader that the Force is very strong with Luke, with Palpatine going ever higher and saying that he has Force Potential to destroy them. Over the couple days of actual training he had with Jedi Masters, Luke manage to become one of the most powerful Jedis to this date. Learning how to find crystal and making his own lighsaber just by looking at one, being to master form V, even though he was never teached by anyone. He was able to overpower even Darth Vader who was considered by many to have been the one of the best swordsman in the galaxy. During the years of his training Luke developed a great affinity with the Force being able to use the both sides without falling to he Dark Side. He was considered a master in telekinesis (being able to push at least 10 men with ease), master in telepathy, Force Speed, Force Vision, Force Grip and many others.
Luke's Force and Lightsaber Skills - Legends
Spoiler :
In the Legends department Luke has shown incredible feats and is generally considered the God of the Galaxy and the strongest character in the Universe. On top of my mind.
Force:
1. Said to have the same Force Potential as Anakin
2. Used both sides
3. Electric Judgement
4. Master of Telepathy
5. Scan and read the minds of entire Solar System
6. Using telepathy he has been able to send a message to every single Jedi in the Galaxy
7. He can hypnotize people, order them to do anything he wants and implant/delete memories
8. Was able to put an illusion of enitire fleet coming, on Caedus who himself was consider as one of the best telepath ever to be born
9. Can make clones of himself
10. Can make himself invisible to others
11. Telekinesis Master
12. Used TK to put Caedus to ground (enormous feat being that Jacen was able to casully move X Wings without effort at all)
13. Used TK to fly Millenium Falcon
14. Used TK to activate every mechanic on a planet
15. Used TK to stop AT-ST (Walkers)
16. Used TK to manipulate movement of torpedos
17. Used TK on an atomic level
18. Master of Speed
19. Can ran several miles under 1 second
20. Has the reaction time of nanoseconds
21. Was able to see a ship going lightspeed in slow motion
22. Speedblitz Noghri and Nightsisters
23. Was able to move so fast that not even the fastest people in the Galaxy could see him
Lightsaber:
1. Has been able to master Forms just by looking into Jedi Holocron
2. Moves lightsaber at such speed that it seemed as he used at least 20 lightsabers at the same time
3. Defeated Vader
4. Defeated Palpatine numerious time
5. Can deflect blasters from AT-ST
6. His lightsaber swing is lighting was
Maybe his biggest powers and feats are:
1. He can acieve Oneness where he truly becomes the one with the Force and cannot be hurt by almost anything
2. Can teleport himself, others, objects and almost anything to any part of the Galaxy
3. Can manipulate weather
4. Can froze any materia (fire, water, ice, wind, lighting..)
5. Alter Environment - Can manipulate reality
6. Can use the Force to seize and vanish f*cking Black Hole
Luke is on of the two major characters prior to the Force Awakens. As it seems he will also have a big role in this one to. So let's talk about Jedi Master a bit.
1. First and the most important question. Will Luke help the alliance or will stay in the Temple?
2. Being that Luke started the new Order he is now its Grand Master and as such its strongest member. In the episode VIII, will Rian Johnson shows us Luke as the most powerful character or will he follow the agenda of Old Jedi Masters who are indeed powerful but are more about wisdom than the power itself.
3. Does Luke know Snoke is? If he does, why wasn't he tried to take him down? He is the most powerful Jedi left, it's his duty. Maybe he is afraid that him too will fell to the Dark Side?
4. Would you like to see any feats from Legends done by Luke shown in the next two movies?