Tsukuyomi

Tsukuyomi is noted to be one of the most powerful genjutsu in existence. It is unique to the Uchiha clan and only those who have awakened the Mangekyō Sharingan can perform it. It is said to represent the, the antipode to Amaterasu — a ninjutsu of similar power.

Usage
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.

Infinite Tsukuyomi
The Eye of the Moon Plan involves Madara Uchiha becoming the Ten-Tails' jinchūriki and using its power to reflect his eye on the moon, which allows him to cast an throughout the entire world, creating an illusory world where every aspect is ideal for an utopia, stripping reality of its free will and effectively conquering the world.

Limited Tsukuyomi
In Naruto 6: Road to Ninja, Obito casts a trial version of the Infinite Tsukuyomi, the, on Naruto and Sakura, which provides the alternate reality setting of the movie.

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. Interestingly, as Tsukuyomi is the Moon, he is also associated with the passing of time, and at times cited to be the God of Time (or at least of the calendar), fitting the genjutsu's ability to alter the perception of the passing of time.

Trivia

 * In Naruto: Ultimate Ninja Storm, Itachi uses Tsukuyomi in a different manner. He has the red moon crush the opponent while the image of the moon warps into a copy of his Mangekyō Sharingan eye.