Kamui

Kamui is a powerful dōjutsu that creates a unique and specialised form of space–time ninjutsu, it allows the user to achieve two very distinct, yet closely associated feats — teleportation and "intangibility".

Overview
Kamui allows the user to transfer anything to another dimension. Once a target is sent to this dimension it is unable to escape. This technique, when used through Obito's right eye, is also able to make the user "intangible" by transporting portions of their body to the same pocket dimension. Obito was able to activate Kamui the moment he awakened his Mangekyō Sharingan, while Kakashi, who awakened his Mangekyō Sharingan at the same moment as Obito without realising, didn't have access to it until sometime after Sasuke Uchiha's defection and made first use of it in the series during his encounter with Deidara.

Kakashi Hatake likens the characteristics of this 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 a seal nor a summoning tattoo to be performed. The side of the eye using the technique determines the range and detailed properties.

Teleportation
Each of Obito's eyes is able to transport objects to the other dimension. By creating a swirling distortion, the user is able to open a void into the other dimension. This technique's effect acts as an attractive force, both visibly drawing the target inwards and distorting their form until they disappear, although physical contact is required to absorb a target. After absorbing targets through this process, the user is able to eject them from the eye used at any time of their choosing, demonstrating the ability to eject objects with varying degrees of force. This is demonstated by Obito, who uses it with weapons of various proportions and/or quantity with relative ease and at a moment's notice, giving opponents little to no opportunity to react accordingly.

Another unique trait of Kamui is that it allows the user to teleport to any location they desire, including the other dimension. When using Kamui to teleport living beings, including the user, whatever the target is touching will be warped along with them and their chakra becomes untraceable. Despite not always being present, Obito can keep his targets under genjutsu while they are confined inside this pocket dimension and thus, keep them incapacitated for extended durations.

Left Eye
The left eye's primary use of Kamui is based on line of sight and, as such, does not require physical contact to warp a target into the other dimension (also, Kakashi doesn't centre Kamui around his eye unlike Obito). By focusing to create a barrier space and concentrating on the target within, Kamui will distort space and the target will be drawn into the other dimension. When Kakashi first used this technique, it required great concentration and was difficult to aim, dragging in only Deidara's arm when he aimed for his head. By the Invasion of Pain, Kakashi was able to use Kamui to stop a speeding nail from penetrating his head. Later, during the Fourth Shinobi World War, Kakashi also displayed the ability to teleport himself.

Right Eye
The unique trait of this eye is the ability of intangibility. When activated, any part of Obito's body that overlaps with a solid object is seamlessly warped to the other dimension, making it appear as though he is phasing through them. Using this ability, Obito can dodge most attacks, and by overlapping his entire body into large objects, he can not only conceal himself from view, but erase all traces of his chakra. Obito is also able to enter and travel through the ground using this ability, a characteristic he often exploits to ambush his opponents from below. Though he is unable to establish any physical contact while being intangible, Obito can still use chakra chains. He also seemingly possesses the capability to extend this intangibility to whatever he's touching at the moment of activation, as long as he is able to maintain some form of contact with at least a part of the desired item or person. Obito centres his Kamui around his right eye and also requires physical contact with the target to warp them.

Drawbacks
Since this technique is shared by two different users of the same pair of eyes, both parties can use their own technique to counter the effectiveness of the other, thus making it useless to use against one another directly. Obito can extend this negation to targets outside of his own body, as he negated Kakashi's attempt to decapitate the Demonic Statue of the Outer Path's head. Similarly, Kakashi was able to escape Obito's attempt to trap him in the other dimension.

Left Eye
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 his left eye to bleed if overused.

Kakashi was originally only 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. Later, he became able to use this technique several more times in a single day and attempted to use it to decapitate the Demonic Statue of the Outer Path, although he required a considerable amount of time to prepare the necessary amount of chakra and the technique was ultimately negated by Obito. After being given chakra by Kurama, Kakashi was able to use his long range variant of Kamui to quickly transport a target as large as Gyūki to the other dimension and later eject the tailed beast from his eye, as well as utilise the technique more times than he would usually be capable of. He estimated that the influence of Kurama's chakra, when given directly by Kurama, made his usage of Kamui at least three times more powerful than usual.

Right Eye
In Obito's case, the primary weakness of this technique is that both aspects cannot be used concurrently, as he 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, Obito 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 Obito's intangibility, the sections of his body residing in the other dimension can still interact normally with other objects that are also contained within said dimension, meaning they can be damaged by such items, a characteristic that Kakashi exploited to injure Obito on multiple occasions during the Fourth Shinobi World War. While controlling the Ten-Tails, Obito was unable to extend his intangibility to the beast or his means of connecting to its head, and was separated from it as a result.

Unlike most other Mangekyō Sharingan users, Obito's extensively continuous usage of the Kamui technique does not seem to tire him at the very least, nor even cause his eyesight to deteriorate.

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

 * 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.
 * Occasionally, in the anime, when Tobi goes to absorb his opponent he does not touch them, this is a mistake that the animators made as in the manga there is always bodily contact. A notable occasion of this is when Tobi fights Danzō's bodyguards, he does not have any physical contact with Fū when he absorbs him.