Spite & Malice

While I have a strong belief that Mukuro is full of it when he says that he remembers all his past six lives due to the fact that his right eye was implanted on him by the Estraneo family and was not naturally born with it, it is true that his skills make a strong reference to the religion of Buddhism and the belief of reincarnation. His ability is called the Six Realms of Rebirth, but note that his name (when written as Rokudo Mukuro) literally translates to Six Paths of Death. He makes references to the unending cycle of life itself. In Buddhism, it is believed that when you die you are reincarnated into one of six forms of life.

Mukuro's right eye changes from the Japanese Kanji of the numbers 1 through 6 depending on each skill. His techniques are based off of these realms:

(一) Nakara Realm: Grants the skill to destroy a person's mind with unending nightmares
This ability allows the user to cast illusions. On several occasions, Mukuro has summoned water lilies in his illusions. Water Lilies, specifically pink ones, are known to be related to the deities or gods on Buddhism. We all know how cocky Mukuro can be.

(二) Preta Realm: The ability to steal the techniques of others
When the user has possessed a body, they may use the person's techniques.

(三) Animal Realm: Grants the skill to summon deadly creatures
There is no evidence of Mukuro summoning any animal but snakes. While Buddhism has depicted snakes in a positive light, most cultures depict snakes as sly and deceitful creatures, for example: Christianity. Like a "snake" Mukuro has deceived someone of innocence like Chrome.

(四) Asura Realm: Increases physical combat abilities
A Dying-Will flame burns over Mukuro's right eye and his speed increases.

(五) Human Realm: Grants extraordinary strength and increases the user's aura
By piercing his right eye, not only is his aura black but also several parts of his skin. Despite being the most powerful of his techniques, Mukuro finds both the realm and the skill repulsive. Humans are ignorant and selfish creatures, and Mukuro has experienced this first hand.

(六) Deva Realm: Grants the skill to temporarily possess another person's body
The user is able to possess another body, but there is a possibility of the host breaking free if their will is stronger.

Mukuro's weapon also plays a role in Buddhism. The trident is a weapon of Shiva, the god of destruction. Satan is also depicted as a wielder of a trident. Wanting to erase humanity, this weapon is fitting for a shady character like him.

Not only is the trident symbolic but it also connects back to the Possession Bullet the Estraneos had created. After the user shoots themselves with the Possession Bullet they now have the ability to possess any living body that was sliced by the blade of the trident. Unlike the Deva Realm which controls the victim, Mukuro is able to have full use of the body. He does not feel the body's pain and can even control several people at once. Like the Dying-Will bullet which can only revive those with regrets, there is a catch; the Possession Bullet is only compatible with those that have a strong will. That really says a lot about Mukuro's sense of ambition to say the least.

Transmigration

The transmigration from one body to another is an ability unique to Mukuro. His possession ability even goes as far as taking over those he has not even met, particularly Chrome Dokuro (also known as Nagi, her given name). Like the possession bullet, the transmigration technique does not work on just anyone. There are no bounds in the spiritual world, hence why Mukuro may drift from body to body with this technique, but the user and vessel must be compatible in spirit or else the technique will fail. Below are pictures of the people Mukuro has reincarnated himself in with the use of this special technique. However, Guido Greco (a.k.a. Leonardo "Leo-kun" Lippi) is still pending on whether or not he was actually a "second" Chrome Dokuro, or in other words another successful vessel at Mukuro's disposal.

         

In Vongola77, a brief story was shown about Mukuro trying out the transmigration ability on a young boy named Mitsuru "Mii-kun" Fugimo. Barely hanging by a thread, Mukuro was lucky to even find someone even slightly close to his spirit, but due to the incompatibility Mukuro is unable to incarnate himself through the boy and Mitsuru's body eventually rejects him. Mukuro was lucky to have found a body like Chrome's to use. It was chance that brought them together, and because of the similarities to their spiritual wavelength Mukuro was able to walk into Chrome's dreamscape illusion and can even telepathically communicate with her.