Skysolo

Skysolo is the slash ship between Luke Skywalker and Han Solo from the Star Wars fandom.

Canon
Luke and Han have a very good relationship in the Star Wars original series, (Episodes 4, 5, and 6).

They first met in Mos Eisley, where Luke was traveling with the Jedi Knight Obi-Wan "Ben" Kenobi on a mission to deliver R2-D2 to Alderaan. Luke and Ben needed a quick ship with no questions asked, and therefore managed to hire Han and his ship, the Millennium Falcon. Han had the full intention of taking his pay after the job and paying off his debt to Jabba the Hutt, but instead found himself roped into the crazy adventures that ensue after Alderaan is blown up by the Death Star.

A New Hope
On the Falcon, after Han, Chewie and Luke rescued Princess Leia, Solo asks Luke if he could ever see Leia and himself together. Luke abruptly says "No" and turns away. There's a moment where

When the rebel base on the fourth moon on Yavin is about to be destroyed as well by the Death Star, and Luke gets recruited as a fighter pilot, Han has the opposite idea. He takes his reward and flies out. Luke seems pretty frustrated and upset that Han is just going to get up and leave, and says that they (the rebels, including him) could use Solo's good piloting skills, and Luke seems to value Solo as a friend. Solo also tells Luke that he could use him, and asks if he wants to come with him and Chewbacca instead. (Of course, Luke declines.) Solo also seems to value Luke.

Later, when Luke is basically about to get killed by Darth Vader and his wingmen while he tries to fire his proton torpedoes, it's revealed that Han came back when he fires on Vader and his men. Solo shoots one TIE fighter, which collides into the other, which knocks Vader out of the fight. Solo later says that he couldn't let Luke have all the glory.

After the Death Star is destroyed, and Luke and company are at the rebel base again, Luke pulls Solo into a hug, which Han reciprocates. They remain within grasp of each other, still holding the other's arms, while Luke says tells Han that he knew he would come back.

The Empire Strikes Back
When Luke gets lost in the icy wasteland of Hoth, Han goes out into the night to save him, and when he finds him, he manages to keep Luke alive and warm until they're both rescued in the morning. Before Han leaves Echo Base to find Luke, he looks concerned (in his way) when he learns that Luke didn't return.

Fandom
FAN FICTION

Trivia

 * It was rumored that on the set of Empire Strikes back, after Luke is rescued and is healing, instead of Han saying "That's two you owe me, Junior,", he kissed Luke instead. Mark Hamill, (the actor who played Luke) tweeted in response: "I never kiss & tell."