Kamui

Kamui is a powerful Mangekyō Sharingan 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 the right eye, is also able to make the user "intangible" by transporting portions of their body to the same pocket dimension. While both awakened their Mangekyō Sharingan, Obito was able to instinctively make regular use of Kamui while Kakashi seemingly didn't become aware of it until some time after Sasuke Uchiha defected from Konohagakure.

Kakashi likens the characteristics of this technique to those of the 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.

Teleportation
Each eye is able to transport targets by creating a swirling distortion that opens a void into another dimension. This technique's effect acts as an attractive force, both visibly drawing the target inwards and distorting their form until they disappear. A user of the right eye requires physical contact to absorb a target, while a user of the left can do so from a distance. Kamui also allows the user to teleport to virtually any location they desire by absorbing their own body into the swirling distortion. When using Kamui to teleport, whatever the user is touching will be warped along with them and their chakra becomes untraceable.

After storing a target within Kamui's dimension, the user can then eject it from their eye at any time. This can be done with varying degrees of force, as demonstrated by Obito, who ejects various weapons at a moment's notice, giving opponents little opportunity to react accordingly. While in Kamui's dimension, the user can transport targets out of said dimension at any time, even without establishing physical contact. Despite not always being present, Obito can keep targets under genjutsu while they are confined inside this technique's pocket dimension, thus keeping them incapacitated for extended durations.

A user of Kamui can synchronise with other space-time techniques, allowing them access to other dimensions. After entering a new dimension through this method, the user is able to travel to and from said dimension, as well as any other connected dimensions, at will.

Left Eye
The long-range version of Kamui, an ability belonging to Obito's left eye, is primarily based on line of sight and, as such, does not require physical contact to warp a target into the other dimension. 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. The barrier can be expanded, as Deidara was forced to fly further away in an effort to escape its effects.

Right Eye
The short-range version of Kamui, belonging to Obito's right eye, requires physical contact to warp a target. However, this eye has a unique variation of teleportation akin to intangibility. When activated, any part of the user'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. This ability can dodge most attacks, and by overlapping his entire body into large objects, the user can not only conceal himself from view, but temporarily erase all traces of his chakra. This ability can also be used to travel through the ground; a characteristic that Obito often exploited to ambush his opponents from below. The user 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. It also allows the user to bypass even the strongest Barrier Ninjutsu, as Obito passed through the one meant to prevent anyone from entering the area where Kushina Uzumaki was giving birth.

Both Eyes
When both eyes are used together on the same target, the teleportation process works twice as fast. Through both eyes, the user can create two distortions at the same time and connect them. This was demonstrated when Obito first used the long-range Kamui to synchronise with another dimension, and then used the short-range Kamui to teleport himself, and/or any one touching him through the portal.

To bolster up the rapidly crumbling portal linking two spaces, a second eye almost quickly accompanies following the opening. A move that causes substantial bleeding from the strain induced eyes. The amount of required chakra pushed Obito to the limit despite even huge portions already being coursed through him from Sakura.

Drawbacks
Since this technique was shared by two different users of the same pair of eyes, both parties could use their own technique to counter the effectiveness of the other, thus making it useless to use against one another directly. Obito could extend this negation to targets outside of his own body by concentrating on the warped space, as he negated Kakashi's attempt to decapitate the Demonic Statue of the Outer Path. Similarly, Kakashi was able to escape Obito's attempts to trap him in the other dimension and influence attacks to hit the former should he attempt to phase through them.

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 put Kakashi's body at risk as well. As his Sharingan was transplanted, usage of this technique posed an even greater risk to Kakashi. Similar to Amaterasu, repeated use of the technique puts a great deal of strain on the user, which can cause the eye to bleed when overused.

Kakashi was originally only able to use this technique up to three times a day before being rendered immobile, and his aim and control over the size of the barrier were 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, as well as 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 transport a target as large as the Demonic Statue's head, though doing so required time to prepare the necessary amount of chakra. After receiving chakra from 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.

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. In order to bypass this weakness and remain in Kamui's dimension for a longer duration, Obito has to "solidify" and absorb his entire body. She also revealed 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. After becoming the Ten-Tails' jinchūriki, Obito noticed that he could no longer use Kamui's ability to let objects slip through him. Madara, who was able to teleport himself as the Ten-Tails' jinchūriki into the Kamui dimension, proved that this part of Kamui still works.

As shown numerous times with both eyes, if Obito uses Kamui in another dimension that isn't his, it uses a huge amount of chakra and causes even Obito's, the original user's, eyes to bleed.

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

 * Unlike other Mangekyō Sharingan users, Obito's continuous usage of Kamui does not seem to cause his eyesight to deteriorate.
 * In the sixth movie and several anime episodes, Obito is shown to be able to access Kamui without having his Mangekyō Sharingan activated.