Daughter of Smoke and Bone was written by Laini Taylor. I'm not sure if it's strictly YA because the heroine is a college student. The main character Karou is an art student living in Prague and running errands for her employer, Brimstone. She has bright blue hair and constantly draws monsters in her sketchbook. My favorite parts are when Karou is a child and interacts with her makeshift family of Brimstone and Issa. That's probably why I enjoyed the first part of the book more than the last which focuses on her relationship with Akiva, the avenging warrior-angel. I love romance as much as the next person, but the childhood scenes are pure magic.
As for this trailer, I loved seeing the monster sketches in this video. The most amazing part of the book is the world-building that unfolds so brilliantly. I think this trailer illustrates that quality well.