First of all, as a 50 something Japanese who experienced what is was like living in Tokyo back in the late 80's, I was really surprised the authenticity of the depiction of the period. They recreated the era so perfectly, it was easy for me to get into the story and take them seriously. That's not always happens when hollywood pictures try to portay my country. Good start.
And yes, as other reviewers points out, the story goes very slow, and they reveal the bare bones much much later, so sometimes it's a little difficult to follow and understand what's happening. But we will come to know the loneliness and anxiety of this caucasian woman from Sweden who lives in Tokyo bit by bit, and what happened to her life in the past, our patience will be nicely rewarded. This film is like a kind of psycological charachter study which disguises as a murder mystery. Maybe not for everyone's taste but I'm sure some people may find it interesting and fascinating.
Alicia Vikander's performance is wonderful as always and she speaks Japanese language maybe not so perfectly but beautifully. Naoki Kobayashi also did a fine job considering his low experiences as an actor which I'm looking forward more to come.
And nice surprise was a brief appearance of Yoshiko Sakuma who was one of the most popular beauty queens from the golden age of Japanese cinema and also one of the two divas (the other was Junko Fuji) of Toei Studio in the 60's.