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.

According to Itachi, while on Tsukuyomi he controls time and space.

Tsukuyomi means "God of the moon". Tsukuyomi requires eye contact to be performed. When executed, the jutsu traps the target in an illusion that is completely controlled by the user. Itachi's prowess with the technique has allowed him to alter the perception of time with ease within the genjutsu to make it seem to last for days when in fact it only lasts a few seconds. This allows him to torture the target for what seems like days on end, causing mental trauma that will render them unable to fight for an extensive period of time. 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 a grayscale, inverted color.

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 but had little to no effect on the stress that is put on the eyes, leaving Itachi perfectly fine after performing it despite his loss of chakra. According to Kakashi, Itachi's 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's version is much weaker than Itachi's, he couldn't manipulate the time in the illusion and Danzo was able to break it with a simple Genjutsu Release. Despite this, he used it to fool Danzo into believing the Izanagi was still active to beat him.

Madara Uchiha's Eye of the Moon Plan involves acquiring the Ten-Tailed Beast's power and body in the moon, which allows him to cast an throughout the entire world, effectively letting him conquer it.

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.