Currently on episode 13/13
I don't think this anime can be properly appreciated with out watching K: Missing Kings Movie between episodes 1 and 2. Because there are huge bits of info "missing" between the first 2 episodes. The movie isn't a prequel. It fits directly in between episodes 1 and 2 and explains what happens Mikoto and how Anna becomes the new Red King. What happened to the Gold King and the Gold clan members. As well as other pieces of key information related to the events leading up to the 4 episode.
I love everything about this series so far. It's exciting to watch, the fight scenes are some of the best I've seen in a while, most of the characters are already pretty powerful so not a whole lot of room for growth, but we're talking about a series with 7 kings and their vassals so they have to be OP from the start because there are only 13 episodes and the 1 hour long insert movie so some things need to already be understood about the story line. Lengthy character development should be left for series exceeding more than 20 episodes. There just isn't enough time to explain every single little detail in a shorter series.
*edit* So with the series wrapping up it's final episode I have to say I enjoyed it very much. For those of you that haven't watched it yet but are interested in doing so, you should know that K is part of a larger project so get the full experience watching the Missing Kings movie is a must. Even though the movie is a year older than Return of Kings it's not a fucking prequel but an insert for Return of Kings.
I recommend watching the movie after the first episode of Return of Kings. Then the second episode as it was probably intended. For whatever reason it was produced this way, the movie takes place after the first episode and before the second of Return of Kings. Explaining most of the gaps in the story between eps. 1 and 2. Also there are a few manga that go with the events of the entire K project.
"K - Countdown" is a must read it takes place after the events in the movie and contains the information and character viewpoints after Mikoto's death. (8 chapters)
"K - Stray Dog Story" - Kuro's story (5 chapters)
"K - Days of Blue" - Scepter 4's story (10 chapters)
"K - Memory of Red" Homra's story (15 chapters)
"K - The First" Shiro and the Gold Kings story (16 chapters)
I highly recommend watching this anime it's so good. So far 9/10 overall from me. Thank you for reading! Enjoy the show! ^_^