Horcrux
"Of the Horcrux, wickedest of magical inventions, we shall not speak nor give direction–"
—the introduction of Magick Moste Evile
A Horcrux is a very powerful object in which a Dark wizard or witch has hidden a fragment of his or her soul for the purpose of attaining immortality. Creating a single horcrux allows one to gain the ability to resurrect themselves if their body is destroyed, but the more horcruxes one creates, the closer one is to achieving true immortality. Creating multiple Horcruxes is suggested to be costly to the creator, by both diminishing their humanity and even physically disfiguring them. It is possible to put the wizard's or witch's soul back together, but it is excruciatingly painful.

Origins
The first Horcrux was created by Herpo the Foul. The only other known creator of them was Lord Voldemort, who went on to create multiple Horcruxes and Dumbledore believed he was the only one ever to do so. Others have tried with mixed results, some even dying in the process.

Nature
Slughorn: "Well, well, it can't hurt to give you an overview, of course. Just so that you understand the term. A Horcrux is the word used for an object in which a person has concealed part of their soul."
Riddle: "I don't quite understand how that works, sir."
Slughorn: "Well, you split your soul, you see, and hide part of it in an object outside the body. Then, even if one's body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged. But, of course, existence in such a form...few would want it, Tom, very few. Death would be preferable."
— Horace Slughorn and Tom Riddle discussing Horcruxes
Creation of a Horcrux is considered the foulest act of Dark magic, as it attempts to violate and tamper with the multiple laws of nature and morality in its creation. Horcruxes are objects considered to be so evil that even the texts published explicitly to cater to the practise of the most terrible kinds of magic will not speak of them. Even Magick Moste Evile skirts the topic.

Reconciliation
Ron: "Isn’t there any way of putting yourself back together?"
Hermione: "Yes, but it would be excruciatingly painful."
Harry: "Why? How do you it?"
Hermione: "Remorse. You’ve got to really feel what you’ve done. There’s a footnote. Apparently the pain of it can destroy you. I can’t see Voldemort attempting it somehow, can you?"
— Ron Weasley, Harry Potter and Hermione on reconciling the fragments of a broken soul
The creation of a Horcrux can be reversed by its creator through truly feeling remorse, though the effects of this can apparently be painful to the point of being fatal. However, as is described below, this may be a far preferable outcome than the alternative.
Interestingly, since Dumbledore said that "there is no help possible" for Voldemort's soul, it may be that any soul as badly damaged as Voldemort's could no longer be repaired through remorse as described in Secrets of the Darkest Art. Alternately, and more likely, the soul can still be repaired through the redemptive power of repentence. Harry told Voldemort to "try . . . be a man. . . try for some remorse. It's your one chance. It's all you've got left." This seems to indicate that though Tom Riddle's soul is maimed and seriously injured, he can still repair it by regretting all the horrible things he did, as Gellert Grindelwald did in later life.

Destruction
Harry: "So if all of his Horcruxes are destroyed, Voldemort could be killed?"
Dumbledore: "Yes, I think so. Without his Horcruxes, Voldemort will be a mortal man with a mained and diminished soul. Never forget, though, that while his soul may be damaged beyond repair, his brain and his magical power remain intact. It will take uncommon skill and power to kill a wizard like Voldemort, even without his Horcruxes."
— Harry and Dumbledore discussing how to destroy Voldemort
Horcruxes can also be destroyed by others, seeing as the piece of the soul depends upon its container to survive; the opposite of a human being. Destruction of a Horcrux is difficult, but not impossible, and requires that the receptacle to be damaged completely beyond physical or magical repair. When a Horcrux is damaged to this point, it may appear to "bleed" (ink in the case of Tom Riddle's Diary and a "dark blood-like substance" in the case of Ravenclaw's Diadem) and a scream may be heard as the soul fragment perishes.
It is unknown if the creator of the Horcrux will be able to sense that his soul fragment was destroyed, although Dumbledore stated that in the particular case of Voldemort, he wouldn't feel their loss because his soul was sliced too many times and stayed that way for too long.
All known methods of Horcrux destruction are as deadly as the creation. For example, the earliest known method is administering basilisk venom to the Horcrux, the procurement of which is next to impossible. Other known methods are Fiendfyre (as evidenced by its destruction of Rowena Ravenclaw's Diadem), which requires extreme skill to control and the Killing Curse (extremely Dark magic) which seems to be capable of destroying a Horcrux if it is animate, given that part of Voldemort's soul contained in Harry Potter was destroyed when he was struck with the Killing Curse in 1998. However, Harry Potter was never a true Horcrux (see below) and so it may not work on a proper, animate Horcrux (like Nagini), probably having unforeseen side effects.
The seventh Horcrux (Harry Potter) was not destroyed in the Chamber of Secrets because Fawkes' tears saved him and hence the "receptacle" (Harry) was not then destroyed beyond repair.
Albus Dumbledore, Ron Weasley, and Neville Longbottom used Godric Gryffindor's Sword to destroy Marvolo Gaunt's Ring, Salazar Slytherin's Locket, and Nagini respectively. This was only achievable as the sword is a Goblin-made artefact, which can absorb qualities that strengthen it. When Harry Potter slew the Basilisk in the Chamber of Secrets, the sword was imbued with Basilisk venom and became capable of destroying Horcruxes.
Harry Potter and Hermione Granger used Basilisk fangs from the Chamber of Secrets to destroy Tom Riddle's Diary and Helga Hufflepuff's Cup, respectively.

Powers
Ron: "The bit of soul in that diary was possessing Ginny, wasn’t it? How does that work, then?"
Hermione: "While the magical container is still intact, the bit of soul inside it can flit in and out of someone if they get too close to the object. I don’t mean holding it for too long…I mean close emotionally. Ginny poured her heart out into that diary, she made herself incredibly vulnerable. You’re in trouble if you get too fond of or dependent on the Horcrux."
— Hermione on a Horcrux's ability to possess and eventually control a person
The fragments of a person's soul within a Horcrux can think for themselves and have certain magical abilities, including the ability to influence those in their vicinity. When Harry, Ron, and Hermione were carrying Salazar Slytherin's Locket around their necks in 1997, they each became moodier and more prone to fighting, especially Ron. They were also unable to summon their Patronuses while wearing the locket since the soul fragment inside was darkening their thoughts. A person with an affinity for the Dark Arts, on the other hand, would be strengthened by the influence of a Horcrux, as Dolores Umbridge was when wearing Salazar Slytherin's Locket. If a person is more emotionally vulnerable, it is possible for the soul inside the Horcrux to take control of him or her, as Tom Riddle's Diary did to Ginny Weasley. In fact, Voldemort took advantage of this possessive power to reopen the Chamber of Secrets, using the diary as a weapon rather than a safeguard.
In this way, a Horcrux can gradually feed on another person's life or negative emotions to strengthen itself and increase the ability of the soul fragment within to act independently in the physical world. The best example of this is in the case of Tom Riddle's diary. For decades, the diary lay dormant in Lucius Malfoy's possession, doing nothing other than safeguarding the soul fragment of Tom Riddle. When Ginny Weasley began to transcribe her fears and insecurities into the pages of the diary, the fragment of Tom Riddle's soul contained within was not only able to write back to Ginny but eventually drained enough life out of her to actually manifest itself in a semi-corporeal form and work magic with Harry Potter's wand.Likewise, Salazar Slytherin's Locket slowly gained power when it was in the possession of Harry, Ron, and Hermione in the months prior to its destruction. It can be theorized that the locket gained somewhat less power from them (not enough for Riddle to fully manifest but still enough to speak and create illusions) because Harry, Ron, and Hermione were actively resisting the locket's influence instead of embracing it as Ginny had done with the diary. On the other hand, Horcruxes which have been isolated for long periods of time (such as Hufflepuff's Cup and Ravenclaw's Diadem) were very passive by comparison and took no real measures to protect themselves. Even Slytherin's Locket was fairly inert when it was initially discovered in a cabinet in the drawing room at 12 Grimmauld Place, displaying no powers other than being impossible to open.Horcruxes also possess some last line of defence against destruction. The fragment of soul within the Horcrux seems to be able to sense impending threats and can act to defend itself. For instance, Slytherin's locket viciously taunted Ron Weasley with visions of his deepest fears and even attempted to strangle Harry Potter

Side effects
"Tamper with the deepest mysteries - the source of life, the essence of self - only if prepared for consequences of the most extreme and dangerous kind."
—the first of Adalbert Waffling's Fundamental Laws of Magic
To create a Horcrux is to divide one's soul - the "essence of self" - and it is therefore in the creation of a Horcrux that one falls prey to Adalbert Waffling's first Fundamental Law of Magic, the "activation" of which incurs - sooner or later - consequences (or "side effects") of the greatest magnitude.

Dehumanization
One of these such side-effects is the "dehumanising" effect the mutilation of one's soul (the creation of a Horcrux) is said to have. The more Horcruxes one creates, the less human they become, both emotionally and physically; for example, in the house-elf Hokey's memory Tom Riddle is initially shown to be hollow-cheeked but otherwise normal, though ten years later his features look as if they have been burned and blurred, and his skin is extremely white. One can hence assume that in the course of those ten years he had created more than one Horcrux that in turn wrought the physical changes seen in Voldemort over that timespan. Albus Dumbledore believes that no one has ever created more than one Horcrux, with exception to Lord Voldemort.
Of course, this initial consequence of dehumanisation has its own side effect; it logically follows that if one becomes dehumanised by Horcrux creation then they will take less stock of morality in general, increasing the likelihood that they will create another Horcrux, which would in turn make them less human and hence less moral, which further increases their likelihood of making more Horcruxes and so on. In other words, Horcrux creation may be thought of as a "slippery slope" or "downward spiral" until one reaches the limit, at which point no more Horcruxes may be made.

Appearance
One should note that it is unclear whether the red eyes and slit-like nostrils that Voldemort has after he is reborn are caused by having more Horcruxes than he did than when he applied for the Defence Against the Dark Arts post a second time, or whether they are characteristics of a person who has been resurrected with the help of serpents (who have continued to play key roles in his revival). It is probable that he performed these transformations prior to his resurrection as all of his Death Eaters seem to recognise him without question after Voldemort returned.

Instability
A third side effect of Horcrux creation is that the Master Soul itself becomes unstable (even with creating just one Horcrux). The precise dangers of this spiritual destabilization are not currently detailed explicitly throughout the franchise, however, some can be gleaned from the events in the books. For example, the creation of Voldemort's seventh "Horcrux" - Harry Potter - is known to be the direct result of this as when Voldemort was hit by the back-fired Killing Curse at his parent's home in Godric's Hollow it caused his soul to split, with one fragment remaining in him and the other displaced part immediately seeking out the only other living thing in the room and latching onto it - Harry Potter. However, one should note that although this parasitic fragment of Voldemort's soul attached to Harry's has been mistaken for a Horcrux it has been confirmed that in actuality it does not truly constitute one, since it was not created intentionally. Likewise, not all of the known parts of the Horcrux creation process were correctly carried out for it. Voldemort had just committed 2 murders (Harry's parents) so that may have been adequate for that requirement. In this state, Harry Potter may be more accurately described as a "proto-Horcrux", though for simplicity he may be termed a Horcrux regardless.

Limbo
The final known side-effect of Horcrux creation is the inability to move on from Limbo after death. This is seen when Voldemort's Killing Curse (after the destruction of all the other Horcruxes) rebounded and finally ended his life once and for all, his broken and mangled soul was forced to exist in the stunted form of a flayed and mutilated baby that Harry saw in King's Cross during his visit to Limbo, unable to return to the land of the living and unable to go to the land of the dead, because his soul was maimed and unwhole. Reconciliation cannot occur after death, as the soul's state at death remains forever, so the greatest of all consequences incurred by Horcrux creation may be the possibility of eternal limbo of the soul.

List of Voldemort's Horcruxes
"I, who have gone further than anybody along the path that leads to immortality..."
—Lord Voldemort to his gathered Death Eaters after his rebirth

Tom Riddle's Diary
Hiding place：In the possession of Lucius Malfoy, later given to Ginny Weasley (without her knowing it), and eventually found by Harry Potter in the girls lavatory on the 2nd floor.
Created with the murder of：Moaning Myrtle
Destroyed by：Harry Potter
Destruction method：Stabbed with a Basilisk fang
Destruction site：Chamber of Secrets
Date Destroyed：29 May, 1993

Marvolo Gaunt's Ring
Hiding place：In the Gaunt Shack
Created with the murder of：Tom Riddle Sr.
Destroyed by：Albus Dumbledore
Destruction method：Cut with Godric Gryffindor's Sword
Destruction site：Headmaster's office
Date Destroyed：July 1996