Spoiler!
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SPOILER!
Going to make this short. From what I understand when I was reading the raw of Cat and Dog, Seul-Woo married her for a reason (like most people have expected). He made a promise to the grandfather, I think. There was so papers involved, so it might have something to do with the family business or something. I think the grandfather want Young-Woo to marry Seul-Woo because of what happened in when they were younger. The grandfather saw something in the young Seul-Woo. Young-Woo found out near the end and it shattered her entire world. A lot of things happened in between the time before she found out.
Seul-Woo and Young-Woo moving out and into a rooftop apartment. The best friend confessing to Young-Woo. Seul-Woo meeting with his ex-girlfriend again, leaving Young-Woo alone on the highway. Grandfather getting sick, which lead to the truth of the marriage.
I can't really remember much, and I didn't try to translate what I read. I pretty much just skim through most of it.
The series is already up to chapter 85 on the original website! So much to read.