While making this review, I was trying to keep it as short as possible, keep this in mind. I personally prefer short reviews, with as few spoilers as possible. If you have any questions, please go ahead and ask or Google your question.
The story begins when high school student Kazuki Muto is killed one night saving a mysterious girl from a monster, only to wake up in his school dorm, believing it to have been a dream. However, he soon finds out that dream wasn't a dream at all when a giant serpentine monster attacks him and his sister. Tokiko Tsumura, the girl he saved, explains that the monster is a homunculus. Kazuki had been attacked and killed by it when he was rescuing her. However, she, feeling responsible for him, revived him by placing a Kakugane medallion in his chest, serving as a replacement heart.
The Kakugane, as Tokiko explains, is an alchemical device that, when activated, takes a certain form based on the Kakugane's user, forming a unique Buso Renkin. The Buso Renkin is the only thing that can destroy a homunculus monster. Using this, Kazuki creates his own Buso Renkin (the "Sunlight Heart", a huge lance). Along with Tokiko and her own Buso Renkin (the "Valkyrie Skirt", an execution scythe), Kazuki joins the fight against the homunculi and their master.
There's a lot comedy in this. At least in my opinion. The main reason for the comedy is the character Chouno, Koushaku or as I call him: "Butterfly Man". Corny, I know. You'll understand if you watch the anime.... or look on the picture above. I won't go into detail about the anime, since you got the story description and Wikipedia for that. But I will tell you this: If you like Romance/Action/Comedy or just Action & Comedy alone, this anime is absolutely amazing and I highly recommend it.
You follow Muto, Kazuki (brunette boy in the center) and Tsumura, Tokiko (the blue haired girl on the left) through the great story of Busou Renkin. The Action aspect of the story is top of the line, constantly packed with action yet a good amount of "pauses" keeping you glued to the screen without overdoing it.
On a side-note:
There's a specific detail about one of the main characters (Tsumura, Tokiko) I just love. She's got a battlescar across the face and yet she remain absolutely beautiful. I would say it makes her even more attractive with that scar.
In my opinion, Busou Renkin is an overall 9/10.