Death Note

A shinigami, as a god of death, can kill any person—provided they see their victim's face and write their victim's name in a notebook called a Death Note. One day, Ryuk, bored by the shinigami lifestyle and interested in seeing how a human would use a Death Note, drops one into the human realm.

High school student and prodigy Light Yagami stumbles upon the Death Note and—since he deplores the state of the world—tests the deadly notebook by writing a criminal's name in it. When the criminal dies immediately following his experiment with the Death Note, Light is greatly surprised and quickly recognizes how devastating the power that has fallen into his hands could be.

With this divine capability, Light decides to extinguish all criminals in order to build a new world where crime does not exist and people worship him as a god. Police, however, quickly discover that a serial killer is targeting criminals and, consequently, try to apprehend the culprit. To do this, the Japanese investigators count on the assistance of the best detective in the world: a young and eccentric man known only by the name of L.

(Source: MAL Rewrite)

Death Note: Rewrite

1. Genshisuru Kami (Visions of a God)
A two hour episode of Death Note, mainly a compilation of the confrontations between Light and L, re-edited from Ryuk's perspective with new dialogue and soundtrack along with additional animation that could not be included in the original series.  An Unnamed Shinigami comes to Ryuk to question him about his new story in the human world.
2. L o Tsugu Mono (L's Successors)
This story continues where the previous left off, continuing the story of Light. As the previous special told Light and L's battles, this story does the same with the conflicts between Light, Mello, and Near.  
(Source: Wikipedia)

Light Yagami is a brilliant 17-year-old student, one of the top scorers on his exams in all of Japan. One day as he leaves school, he finds a mysterious black notebook on the ground with "Death Note" written on it. The first thing written inside: "The human whose name is written in the notebook shall die." Light decides to use this to cleanse the world of evil by killing all the criminals. On the scene comes L, ace detective, who's determined to find Light—who the world now calls "Kira"—and track him down, thus bringing us an epic psychological thrill ride.

Death Note Franchise