Mu

"For me, one of the premises of the series is that once a person died, they could never come back to life. I really wanted to set a rule that bringing characters back to life is cheating. That's why death equals "nothingness" … If I had to choose [a theme to express throughout the series], I'd say "Humans will all eventually die and never come back to life, so let's give it our all while we're alive"

- Tsugumi Ohba (Death Note 13: How to Read)

Mu, or Nothingness, is a concept in the Death Note series explaining that all humans, without exception, will eventually die and cease to exist, describing the fact that there is no afterlife in the story.

Overview
The general implication of Mu is that all humans, regardless of their actions during life, simply cease to exist upon dying and are equal in death. These rules are applied to all humans; whether they have used a Death Note or not does not matter.

The Japanese reads more like "after death, the place they go; it's Mu," and in Zen Buddhism, "mu is an answer to a question that depends on invalid axioms." When the rule states "the place they go; it's Mu," it means the question relies on an invalid assumption. They don't go anywhere because there is nowhere for them to go to.

Audio drama
Armonia appears in the audio drama with a slightly expanded role relating to the "afterlife." The audio drama merges the concept of Mu and the Shinigami Realm, and Armonia deals with deceased humans. He tells L's spirit his premature death caused "a lot of paperwork." He's part of an inefficient bureaucracy of Shinigami, so slow it takes over five years to acknowledge L's request to return to the human world. Bored, he tries unsuccessfully to convince L that the afterlife is an illusion created by his soul. However, L's request eventually passes up the chain of command to the Shinigami King.

Death Note Relight
Although a different continuity from the Death Note anime and manga, the Mu rule remains present in the Death Note Relight films, debunking the famous Light Shinigami fan theory.

Trivia

 * When Ryuk appears to Light Yagami and tells him that a Death Note user can neither go to heaven or hell, he is messing with Light to see his reaction. Later upon Light's death, Ryuk confirms the Mu rules to Light, explaining that there is no heaven or hell.