I might be a little behind the times, but I'm going to rave about how much I love the Kylo Ren character in The Force Awakens! The key draw for me is how conflicted his character is. Everybody loves noob villains. Because they represent a very real human conflict between good and evil, and how the wrong choices lead us to do terrible things. And they also show how sometimes what's good and what's evil isn't so obvious.

My favourite Kylo Ren scenes:

1. When he first took off the mask
He sure took his time removing the mask, because it was a rather dramatic moment, so that gave me time to imagine what I would see beneath the mask. I was expecting somebody a little more rugged and experienced-looking, with some harsh wrinkles and perhaps an ugly scar down his eye, because that's what I imagined his face to be from how imposing and powerful he seemed, with his mask on. And also how unbalanced he was, wrecking equipment just to vent his rage. An unbalanced person probably would have some corresponding scars on his face, from creating so much damage , right? Or if not a scar, perhaps some manic eyes, like General Hux's eyes--wonderfully portrayed by Domhnall Gleeson I thought!
Instead when he took off his mask, I saw this pale-faced, wide-eyed guy who looked like he just became Kylo Ren a day ago. A whoa moment for me. Some part of me almost expected him to become a normal young guy again and rescue Rey.
So this disjunction between his character and looks really helps to portray his inner conflict between light and dark.

2. When his dad confronted him (duh!)
I was spoilered for this scene (-.-), so I was 100% certain Han Solo was going to die a horrible death. But when he spoke to his father (probably for the first time--and last-- in eons) about his inner pain and conflict just as the setting sun was putting its last rays through the windows, I could totally see so much pain and confusion in his eyes. My heart broke for this terrible villain, just for that split second though, because the next split second he did the unthinkable. Great acting there.
This scene also shows how very much alone he really is: standing on that narrow road in the abyss, being alone in his inner struggle.

3. When he fought with Rey
Actually I like this scene also because it shows that Rey is his equal when it comes to talent in the Force, and perhaps even much more with some training. I love this wave of girl power riding through cinema. And the industry knows girls love it.
This scene also shows a more human side of Kylo. There was a moment when he could easily have finished her off-- his lightsaber was pressing down on her lightsaber, and she was on the edge of a cliff. But! He stopped and offered to teach her. Though she refused after that, with a lot of sass in my opinion. Perhaps I'm getting carried away. But this scene shows how even villains would want a companion and could be human in the most unlikely of times. If she took up his offer he could finally feel less alone in his dark pursuit. Or perhaps he thought it was a waste of life, since Rey was a force-sensitive being? Brings me to the next point!

Which is, how are they related? Kylo acts as if he knows who she is, and this is quite a conceivable theory since he treats her quite nicely, in comparison to his treatment of other people. The 2 competing theories on the net are a) they are siblings; b) they are cousins. I personally think they are cousins (i.e. she is Luke's daughter). It does not make sense for Han and Leia to not know that they have a daughter. Or for Leia to go to all that trouble to hide a 2nd pregnancy from Han, in order to protect the identity of her child? Besides, my personal preference is for poor lonely Luke to have a child of his own. So he can train another Jedi anew, after he presumably failed in his earlier attempt to train Kylo Ren. But why he abandoned his daughter on some desert planet is still a mystery.