Kamui

Kamui is a powerful dōjutsu, originated from the Mangekyō Sharingan of Obito Uchiha, it allows the user to transfer anything to another dimension. The databook entry noted that if one spends a lot of time and trains one's chakra over and over again, this technique can be invoked.

The two users of this technique — each possessing one of the same pair of Mangekyō Sharingan — use this technique in different manners. Kakashi Hatake uses this technique for long-range fighting, warping objects to the other dimension while Obito uses it to teleport himself, or anything he touches to the said dimension; the latter of which is implied to be inescapable once there. Obito is also able to make himself "intangible" by transporting portions of his body to the same pocket dimension.

Overview
This technique is a unique and specialised form of space–time ninjutsu that allows the user to achieve two very distinct, yet closely associated feats – teleportation and "intangibility". Kakashi Hatake likens the characteristics of the technique to those of Minato Namikaze's Flying Thunder God Technique, but notes that it seems to be much more versatile since it requires neither seal nor a summoning tattoo to be performed.

Teleportation
In Kakashi's usage, the target is enveloped with a barrier space and the user concentrates their mind to what they gaze at. The target can struggle helplessly, but against this technique no defence is possible. When the technique is invoked, the space at the centre of the barrier is distorted and the target inside the barrier is drawn in completely. The location and size of the barrier can be specified at will. It is a dreadful technique that, with skilled use and enough chakra, can even pull an entire human being into another dimension.

During the Fourth Shinobi World War, Kakashi learned there is a connection between his technique and Tobi's own space-time ninjutsu as the latter turned out to be his thought-to-be-dead comrade, Obito Uchiha and thus share access to the same alternate dimension through their respective techniques. After learning of the connection, Kakashi teleport objects into the other dimension to hit whatever part of Obito exists there to counter his intangibility. Obito later confirms his technique to be Kamui as well, stating that he'd show Kakashi its "true power".

In Tobi's usage, by creating a swirling, spatial distortion centred upon his right eye, he is able to enter a dimensional void and teleport himself to another location instantaneously, exiting this void in a similar manner to how he entered. During this process, Tobi's chakra becomes untraceable until the teleportation is completed. By his own admission, Tobi can locate anyone and teleport to their current destination regardless of their whereabouts, evidenced by how he immediately found Taka as they were travelling to Konohagakure, as well as Minato Namikaze, who himself had teleported away from Tobi.

Similar to Kakashi's usage of the technique, Tobi is also capable of teleporting other people or objects to a separate dimension, through the same swirling pattern, centred upon his right eye. However, instead of teleporting the targeted component, this technique's effect acts as an attractive force, both visibly drawing the target inwards and distorting their form until they disappear. After absorbing targets through this process, Tobi is able to eject them at any time of his choosing, with varying degrees of force. In doing so, he is able to attack using weapons of gigantic proportions and/or quantities with relative ease and at a moment's notice, giving opponents little opportunity to react accordingly.

Unlike in Kakashi's usage, this form of the technique requires Tobi to make direct physical contact with the intended target, leaving him vulnerable as he cannot be intangible when doing so. Despite not always being present, Tobi can keep his targets under genjutsu whilst they are confined inside this pocket dimension and thus, keep them incapacitated for extended durations.

Intangibility
Using this technique, Tobi is also able to render himself intangible to allow other objects to pass harmlessly through his own body, which he employs primarily to avoid incurring injury from incoming attacks. In actuality, this is but another extension of space–time ninjutsu, where by Tobi instead teleports any part of his body that occupies the same space as another object to a separate dimension. As the transported portions of his body are always obscured by the other objects, Tobi appears completely whole to those observing him. By overlapping his entire body with a sufficiently large object, such as the ground, he can not only conceal himself from view, but also erase all traces of his chakra. Tobi often exploits this characteristic to ambush his opponents from below.

Though unable to establish any physical contact while intangible, Tobi can still use chakra chains. He also seemingly possesses the capability to extend this intangibility to whatever he's presently touching, as long as he is able to maintain some form of contact with at least part of the desired item.

Kakashi's Version
The Mangekyō Sharingan is a dōjutsu that, with continuous usage, burdens the user with the loss of their eyesight. Since this is the source of Kamui, using it in rapid succession puts Kakashi's body at risk as well. As his Sharingan was transplanted, usage of this technique poses an even greater risk to Kakashi. Similar to Amaterasu, repeated use of the technique puts a great deal of strain on the user, causing their eyes to bleed if overused.

Kakashi is able to use this technique up to at least three times in a given day, even when starting at full strength. At first Kakashi's aim and control over the size of the barrier was imperfect. Over time his aim and control improved, as he was able to accurately warp away small and fast moving objects, such as a nail. Kakashi is even able to consecutively warp away two fast-moving arrows.

Obito's Version
The primary weakness of this technique is that both aspects cannot be used concurrently, as Tobi must become and remain tangible in order to transport himself or others, providing a small opportunity in which he is unable to pass through objects and thus, is vulnerable to injury. This deficiency means that he must also materialise when ejecting stored items as well, presenting the same vulnerability. According to Konan, Tobi can only maintain his intangibility for approximately five consecutive minutes at a time, after which he is presumably rendered completely solid for a duration. She also reveals that the time it takes him to absorb something is proportional to its mass, and that it takes longer to absorb himself than another person or object.

Additionally, due to the nature of Tobi's intangibility, the sections of his body residing in the other dimension can still interact normally with other objects that are also contained within this dimension, meaning they can be damaged by such items. As this technique originates from Obito Uchiha's Sharingan, of which both Kakashi and Obito possess one of, the two share the same dimension when teleporting objects, a characteristic that Kakashi exploited to injure Tobi on multiple occasions during the Fourth Shinobi World War.

Influence
Kamui is the word for a divine being in Ainu mythology, although it is almost never written with kanji in modern times. In a more general Japanese context, Kamui refers to the might and majesty of the gods, particularly the Shintō Kami.

Trivia

 * When Kakashi attempted to use this technique on Tobi, he told him not to bother trying as it would be useless. This was probably due to the fact both men where using the same technique, thus sharing the same dimension, making the attack pointless.
 * The Third Databook seems to hint that other Mangekyō Sharingan users can access the technique through sheer training of the eye, though this is unconfirmed.