DN1:

The story begins when Light Yagami, an ace student with great prospects, finds the Death Note, a notebook dropped by a rogue Shinigami death god named Ryuk. Any human whose name is written in the notebook dies, and Light vows to use the power of the Death Note to rid the world of evil. But when criminals mysteriously begin dropping dead, the authorities send the legendary detective “L “to investigate, and he is soon hot on the trail of Light, who must reevaluate his once-noble goal.

Both Light and L believe themselves to be on the side of justice, and the two match wits trying to show exactly which of them is "good" and which of them is "evil."

DN2:

The story begins on the heels of the first movie as Light Yagami joins the investigation team in pursuit of the serial killer known as "Kira." While L still strongly suspects that Light is "Kira," Light tries to uncover L's real name so he can kill him with his Death Note. Confusingly enough, a new rash of murders all around the world are taking place, with a "Second Kira" claiming responsibility. Light learns the identity of the Second Kira and suggests they join forces to get rid of L. Will L be able to
catch "Kira" before he is killed?