I'm not yet finished reading (about halfway) but I can already say what the manga is like.
The idea itself is nice, but cliche. Girl wants boyfriend, old love shows up and claims her to be hers, they become a couple. Eh, quite boring... However, he's a youkai. All the youkai look really cool, have some interesting backstory and that's the main reason why I continue reading.
After reading the first few chapters I was like "Huh? They love each other? They want to marry? What the f*** ist supposed to happen during the next 70 chapters?!" Well, I'm still wondering about that. Somehow the mangaka was able to drag this story on and on and somehow there come new problems which wouldn't be problems if the characters would just open their mouth once and don't try to solve everything by killing (which is a main trait of youkai according to this manga).
The most ridiculous thing is probably this: Suddenly the main girl's love (Kyou) becomes her math teacher. Why? Well, there's no logic behind that at all! Probably the mangaka wanted to write some scenes at school and didn't know how else to place Kyou there. They don't care at all about their relationship being a student-teacher one. It doesn't even strike their mind that the main girl's parents could find out that her boyfriend and neighbor is also her teacher. I mean, that should be hard to hide, right? Nope, not in this manga.
I was also wondering what this girl did before she reunited with Kyou. She has no personality at all. Her only reason for living is Kyou. She doesn't have hobbies, she doesn't have any likes or dislikes. All she does is love Kyou and cry in every single chapter. Oh, and be chased by evil demons who want to eat her.
Compared to that Kyou is the cool, adult-like, super-handsome boyfriend who is quite perverted and will do anything for his beloved princess (especially kill people who get near her).
All in all, you should only read this manga if you're looking for a manga which 1. you can stop reading in the middle of a chapter and 2. features youkai.
EDIT: I'm finished now and I will not change my mind regarding who should read this only. However, the story became slightly more interesting towards the end. Not the end, not the middle, but that thingy in-between. Especially the side characters showed themselves much and as I expected they're really good. Until the end I don't understand Shou though, seems like he has two personalities...