Tsukuyomi

According to Zetsu, Tsukuyomi is one of the most powerful genjutsu in existence. It is unique to the Uchiha clan and only those with the Mangekyō Sharingan can perform it. It is said to represent the, the antipode to Amaterasu, a ninjutsu of similar power.

Tsukuyomi requires eye contact to be performed, trapping the target within an illusion completely under the user's control. Itachi's prowess with the technique has allowed him to alter the perception of time with ease within the genjutsu to make a few seconds seem like many days as a means to torture the target. This results in the victim suffering psychological trauma that incapacitates them for a considerable period of time. After Itachi used it on Kakashi in Part I, Kisame was surprised that Kakashi's mind was still intact. Only Tsunade has been shown capable of curing this psychological damage.

In the anime during Part I, Itachi's use of Tsukuyomi typically featured a red moon casting a red light throughout the illusion with a cloudy atmosphere, giving the background a blood-red appearance while the victim within the illusion is in depicted in an inverted grey scale.

Such a powerful technique is not without its disadvantages however. Due to the complexity of the illusion and the quickness with which it is executed, an enormous amount of chakra is necessary and an added amount of stress is placed on the left eye, leaving Itachi's vision more blurred. Before using it on Kakashi in Part I, Itachi stated that Tsukuyomi can only be broken by a Sharingan user that shares the same blood as him; as demonstrated when Sasuke overcame Itachi's Tsukuyomi in their battle. Sasuke can also perform Tsukuyomi with his right eye, though his illusion is considered inferior to Itachi's Tsukuyomi since it does not alter the opponent's perception of time indicating he has yet to master it.

Tobi's Eye of the Moon Plan involves acquiring the Ten-Tails' power and body in the moon, which allows him to cast an throughout the entire world, effectively letting him conquer it. However, while it is unknown if Tobi is capable of using the normal Tsukuyomi, Madara Uchiha most likely can as a user needs to have awakened both Tsukuyomi and Amaterasu in order to use Susanoo.

Influence
Pulling from the ancient Japanese myth of Amaterasu, Tsukuyomi, and Susanoo, where when Izanagi washed his face after escaping the underworld his right eye became Tsukuyomi, the Moon god.

Trivia

 * In Naruto: Ultimate Ninja Storm, Itachi uses Tsukoyomi in a different variation where his has the red moon crush the opponent while the image of the moon changes into his Sharingan eye.