Tekkon Kinkreet is an anime that has impacted me in so many ways, I just cannot wait to share my opinion and review it.
Let's just start with a quick summary of it.
I am going to try to keep it short, simple and a spoiler-free review with a pretty basic structure : talking about the art, story, characters and the sound.
All of this aside, let's get into reviewing this adaptation of Matsumoto Taiyou's masterpiece manga "Tekkon Kinkreet"

Treasure Town, a city ruled by the stray cats, two orphans known as Black and White, beating down anyone trying to take their streets, be it a thug or a yakuza.
When mysterious enterpreneurs appear with the intention of tearing down Treasure Town in order to replace it with an amusement, Black and White face their greatest enemies yet. It's left up to Black and his destructive nature to save the city and up to White to save Black from himself.

ART :
Tekkon Kinkreet is an anime with gorgeous animation and a very unique and bizzare art-style.
The backgrounds have amazing detail and the characters are very simple, with properly chosen colors, it has great contrast between the backrounds and characters and is simply a joy to look at.

CHARACTERS :
The best part of the movie, no doubts.
These are some of the deepest and most painfully human characters in any anime, each and everyone fighting his own demons.
Even the side characters have a really good amount of personality and thought put behind them. This all makes up for a convincing story telling.
Great characters have never been a burden to a good premise.

STORY :
The story has a simple premise, made deeper and greater by the characters.
Tons of tension, drama and careful and well thought out plot points with great symbolism.
Tekkon Kinkreet presents some interesting themes, mainly the Yin-Yang symbolism with the main characters, note that the main characters are named Black (Kuro) and White (Shiro), but there is also the theme of coming in terms with one's own self. Which was beautifully shown by Black's inner struggle with the Minotaur. The story/ and characters are the bread and butter of Tekkon Kinkreet.

SOUND:
Just like everything else, the sound is superb.
We have the OST done by Plaid, it's beautiful and fits the tone of the show so well, atmospheric and always plays in the right place at the right time.
The ending theme is performed by Asian Kung Fu Generation and serves for a very fitting song to end it all, with a very calm start, leading up to an emotionally packed chorus and ending it off calmly, just like it started.

The voice acting is superb as well. The voice actors did a fantastic job, there are no exaggerated and unfitting sounds. Some of the most convincing and real voice acting I have heard in an anime.

Do I recommend it? You bet I do!
Tekkon Kinkreet isn't for everyone, it's kinda artsy and attracts a niche audience + not many people can understand the symbolism.
One thing this anime relies heavily upon is the character dynamic between our main characters, Black and White.
So if their dynamic doesn't click with you. There is a high chance you might not like it that much.
But as one of my personal favourites, I'd suggest you watch it either way.