ReiShin

ReiShin is the het ship between Rei Ayanami and Shinji Ikari from the Neon Genesis Evangelion fandom.

Canon
Rei and Shinji have a significant relationship through the series, however it is eventually revealed that Rei is a clone of his mother Yui, and in fact has three iterations throughout the series. Rei dies in Episode 23 and is replaced by another clone of her, which alienates her from Shinji. In End of Evangelion, Rei fuses with Lilith and discusses with Shinji about his traumas and the future of humanity.

In Evangelion 2.0, Shinji gets very close to a much warmer and more open Rei, and many fans believed the movie was going to make it a canon relationship, however in 3.0 she was replaced by another clone and Shinji was left alienated from her again.

Fanon
Fans often debate on whether this relationship counts as incest and if Shinji is better off with Rei, whose views on the fandom range from an uncaring, cold "doll" to a caring, warm and philosophical character, or other characters such as Asuka and Kaworu. The fact that Rei is a clone of Yui, Shinji's mother, is sometimes pointed out as motivation for this pairing to be considered incest. Some shippers like to see Shinji's relationship with Rei as sister-like or mother-like.

Detractors also consider Rei as being enabling of Shinji's proclamatic behaviour due to her own passivity and scarcity of her own emotional needs and her almost complete lack of self-worth as a character that is not entirely human, and thus argue she would not develop a healthy relationship with Shinji, particularly contrasted with Asuka.

Reishin used to be very popular in the early days of the fandom in the late 90s and early 00s, but steadily gave way to AsuShin becoming more and more dominant and, more recently after the Rebuilds, is probably in a third place after KawoShin, though it seems to be becoming more popular again. Like those ships, it is featured heavily in official spin-offs, videogames, and manga, as well as doujinshi from those periods.

Fandom
FAN FICTION
 * Rei/Shinji tag on FanFiction.Net