Void

The Void is the term given to the empty space beyond the generated boundaries of each map. It can be seen through gaps in the lowest layer of Bedrock on maps generated prior to the Halloween Update, but also simply by looking up from ground level, as the sky and the void are one and the same. For this reason, the void is a light source, and its brightness depends on the time. As per a recent update, when lava generates on layer 2, the bedrock on layer 1 below it is replaced by smooth stone, meaning it is possible to enter the void again through much larger entrances than before without hacking.

It is potentially endless, however, falling into the Void causes the player's health to be depleted by about 4 hearts per second, leading to the player's death in 2.5 seconds or less, should he or she drop.

In The Nether, the Void is red. It can be entered if one uses a map editor to make a hole in the top bedrock layer of the Nether.

Entities (mobs and items, excluding the player) entering the Void will be deleted in the following tick (as soon as possible). This may be due to the Void not being part of a Chunk, although it is most likely a deliberate optimisation/crash prevention method implemented by Notch. Blocks cannot be built on the underside of the Bedrock layer, and although Water and Lava appear to flow into it, they will not actually spread and form beneath the lowest layer. This prevents players from descending into the Void safely via swimming.

There is currently a bug in SMP that will remove chunks client-side, so while the data is still there, the client cannot see it and will glitch if they step on it. This can be fixed by reconnecting, placing a torch next to the missing chunk or changing the fog distance by pressing F. If you ride a Minecart into this missing chunk, and then you step out of the Minecart, you will fall to the void and die, regardless if you disconnect and reconnect.

Light cannot travel out or through into The Void.

Destination
In a map generated prior to the Halloween update, it is possible to find holes in the bedrock that lead into the void.

A second way exists, but is painfully slow. To start with, find a large cavern. Then find a deep magma lake. The deepest part of the magma lake reaches the bottom layer, and replaces the bedrock which is usually there with stone; if you can get through the entire magma lake and dig through the bottom, you will reach the void.

The last way is with a mod, specifically Single Player Commands. Once it's installed, press the chat button and type: /tele 0 0 0 and press enter. You will teleport below the bedrock level, in the void the map.

Additionally, in theory, the player could walk all the way to and through the Far Lands to the point where the block physics cease to function. At this point all they have to do is take another step and they will plummet through the world into the Void. However, this isn't feasible because it would take an unbelievably long time (walking 32,000,000 blocks) and Minecraft would hang or freeze.

Trivia

 * If you open a hole to the void and block off all light sources, you can see that the void does in fact give off light. However, the bottom of the bedrock on the last layer is completely dark.
 * When you fall through the void, you don't get hurt until you reach the Y-coordinate of -64, and then you get hurt for four hearts per second.
 * When you fall into the void, on a server with anti flying measures, you are kicked, due to flying.
 * In previous versions of the game, anything that goes in the void became invisible. Since Beta 1.6, things that fall into the void become black because there is no lighting in there.
 * It can now be revealed in 1.6 that all entities that go into the void will be destroyed, including dropped items, vehicles and mobs.
 * Riding a vehicle into the void will result in the player being stuck in the vehicle until he/she dies.
 * In 1.8, the void is filled with particles. (at 16:30)

Reference
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