TL:DR
If sci fi, parallel universes, time traveling shenanigans, a touch of magic, a nerd mathematician/prince hero with a white horse and a hot bodyguard/BFF are your jam, dive in.

Frankly I didn't understand the criticism this drama got, then it clicked: people have wrong assumption about it,thinking is a fantasy romance, while is pure Science Fiction with a romantic storyline.

It starts slowly because it needs to build two separate worlds, introducing all the characters, etc. Must be said i found the Kingdom of Corea (KoC) scenes, characters and plotlines better executed, the Republic of Korea (RoK) parts in the first 3/4 episodes are boring.

There are obvious editing mistakes in the first half, that contribute to the initial confusion. The crime investigation seem pointless, because the show didn't made immediately clear the connection between the first dead body in RoK and the doppelganger in KoC. Same must be said about the crime unit characters, with Kang Shin Jae being a complete waste of screentime, especially all his solo scenes, disconnected from the main plot.

It was also very hard for me to like Jung Tae Eul character, not Kim Go Eun fault, who did well in the dual role. Is just I hate when "strong female character" means acting like a man. She was excessively rude, a borderline jerk. That's not being strong, that's being an a**hole, is hard to empathize with her.

I liked Lee Gon a lot more. A well adjusted orphan. A just, loved ruler. A dork, a genius mathematician. A earnest man. Even when he said cheesy things like "this face is my present for you". I wasn't his fan before, so Lee Min Ho surprised me. One example: the king pain over the uncle death and the consequent rage scenes were amazing, he did an outstanding and intense performance there.

Kudos to Woo Do Hawn, he was a real scene stealer throughout all the 16 episodes. It was a bit underused in the middle, but got his shiny moment in the finale., I'm also his fan now.

Episodes 11-12 are still my favorite. The 2 hours worked almost like a solo movie.
The rescue scene with the cavalry charge and the king slaying his enemies? Perfect. From the way it was shot, edited, the score, all so well done, I didn't expected such quality in KDrama.

Cinematography, scene composition and framing: top notch. 18 hours visual fest. Sadly the editing from episode 1 to 10 is not on the same level. So many missed opportunity to leave visual clues to the audience. There is an obvious shift in quality in the second half.

The songs are great. The score is so good, I'm going to listen the various themes on repeat. Gravity, the King and The War is Over are my favorite.

All in all, recommended with a caveat: I don't agree to those who say you need to be extra intelligent to understand this drama, but you do need to pay attention to details all the time.