|Name:||Fushigi Yuugi (ふしぎ遊戯)|
|Date(s):||1992-1996 (manga), 1995-1996 (anime), 2003-2013 (Genbu Kaiden)|
|Country of Origin:||Japan|
|External Links:||author's website (Japanese)|
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Fushigi Yuugi is the story of a pair of normal Japanese schoolgirls who get sucked into Ancient China through a mysterious old book. They each become the priestess of a god (Suzaku and Seiryuu) and must try to summon them with the help of the gods' seven celestial warriors. The girls are forced to become enemies because they are the priestesses of the gods of rival countries. Over the course of the series, they discover that two other girls a generation before had the same experience.
The vast cast of characters from at least four time periods means that the fandom has vast numbers of different pairings of all flavors. Ship wars are (or were) common, and there are large contingents of canon pairing shippers, alternate straight pairing shippers, and yaoi/slash pairing shippers.
The four main gods will be familiar to fans of other series including Onmyouji, Yami no Matsuei, Yuu Yuu Hakusho, and many others. They are Suzaku, Seiryuu, Genbu, and Byakko. These are four direction guardians from Chinese mythology and also correspond to four constellations.
The teams of seven celestial warriors take their names and characteristics from other constellations associated with these four.
In 2003, Yuu Watase created a prequel to the original series called Fushigi Yuugi Genbu Kaiden that follows the story of Takiko, the priestess of Genbu and first of the four priestesses to be transported into the world of the book. The series was completed in 2013 with 12 volumes. While taking place in the same universe, the time period and location are different from the original series. The series never managed to grow to its predecessor's same level of popularity in fandom during it's run and an anime was never made. Characters and events from this timeline are briefly touched upon in the original series.
Yuu Watase has expressed interest in creating another prequel to Fushigi Yuugi for the priestess of Byakko. A oneshot prequel was released in February 2015 but a date for the series's release has yet to be confirmed. It started in 2015, but with a story mostly unrelated to Byakko (though it provides an origin story for the Seiryuu warrior Miboshi).
The fandom was heavily comprised of bishounen fans who watched mainly to see the beautiful boys in action, or romance fans who were hooked on Miaka and Tamahome's love story. Miaka-bashing was a popular sport among the former crowd, leading to strong defenses of the character. 
Nuriko, one of the most popular characters in the series, is clearly intended as an okama--a Japanese word (slur, really) that refers to effeminate, usually homosexual, exceedingly camp crossdressing men. Like most okama in Japanese pop culture, Nuriko doesn't map well onto Western notions of gender and sexuality, which results in multitudinous interpretations of the character and frequent flamewars in English-speaking fandom. Like other okama, he is also an offensive caricature in many ways, though he is unusually developed and sympathetic compared to characters in series like One Piece.
The central canon romance is Tamahome/Miaka. This couple is both popular with fans and widely parodied for their tendency to say each other's names over and over (which was a big anime trope in the 90s).
Pairings with Nuriko are also very popular.
FY features a Twincest pairing of Amiboshi and Suboshi.
Reincarnation and AUs
The bulk of the plot takes place in Ancient China (or an alternate reality Ancient China?), and numerous popular characters die over the course of the series. In addition, the canon itself makes use of reincarnation to grant some of the characters their happily ever after. This has led to a significant number of fixit stories involving reincarnation, usually to present day Japan or wherever the fic author is from.
- Wikipedia's article has more details