Kylo Ren is the anti-Luke (Star Wars Episode VII: The Force Awakens)

Luke Skywalker is a learner of the force after his uncle and aunt are killed by the Empire. He wants to destroy the Empire the whole way through, especially after they kill his friends, including his father, aunt, uncle, mentor, and best friend. Then defeats them in the end of Star Wars/Episode IV.
In Episode V, he ironically finds out that his father is his enemy.
In Episode VI, with another friend/mentor loss in Yoda, he must make the decision to save his family and possibly betray what he's stood for, or destroy his family, and keep himself intact.

Warning: the following is not for those who use the Red Letter Media interpretation of the Kylo Ren character. If you believe in their interpretation, do not continue.

In Episode VII, Kylo Ren is introduced as an anti-Luke Skywalker. Luke Skywalker, is a master Jedi Knight mentor, Kylo Ren is a First Order Sith Apprentice. Luke Skywalker is a man who prides in family, Kylo Ren is a man who wants to get out of the shadow of his non-Jedi father, un-Jedi educated mother and become his own man, a Sith. He disobeys the teachings of his Uncle, Luke, and takes a much different path from where Luke did in Episode IV from there.

In Grand Leader Snoke's first appearance in the film, he basically implies a test for Ren, where his father, Han Solo could get in the way of his Sith training. This adds the stake for Ren encountering Solo at the end of the film.
In addition, Solo previously offered Rey a position on the Millenium Falcon, a position Rey denied. She has a chemistry with Solo, enjoys Chewie's company. is a great pilot and mechanic, but wants to stay on Jakku to see if the family who left her will ever come back. Finn wants to leave the First Order's territories; Rey wants to stay on Jakku. She's young like Luke was in IV and is a hybrid of former Star Wars characters.
Rey and Ren play off each other and the theme of family in the film, as Rey is waiting to find out why her family abandoned her and Ren purposely abandoned his family. Rey is a Jedi; Ren is a Sith. In the scene where Ren attempts to get secrets out of Rey, Ren mentions Rey feeling that Han Solo is a father figure to Rey. Rey becomes a new co-pilot for the Millenium Falcon.
And of course, the Rey-daughter theory that everyone talks about which doesn't necessarily need to happen.

In contrast to Red Letter Media's interpretation that Ren is a sequel to prequel Anakin, and a line that is in the film that pretty much ruins this theory, (where he praises a Darth Vader mask,) I'd pretty much just go with and retcon that Ren is about pride. He doesn't want to be in his family's shadow, with Han and Leia, doesn't want to be on the light side like with Luke and family, and wants to be his own man. I feel like that's a much more powerful interpretation of him not wanting to become a Jedi like his father wanted.