Joshneku

Joshneku is the slash ship between Yoshiya "Joshua" Kiryu and Neku Sakuraba from the The World Ends With You fandom.

Canon
Joshua selected Neku as his Proxy in his three-week long game with Kitaniji. Joshua did so because he saw Neku as being similar to himself (a misanthropic loner with a dislike for humanity) and wanted to prove that if Neku couldn't change, neither could Shibuya (as for Shibuya to change, its Composer, Joshua, would need to as well).

In the second Week of the game, Joshua forcibly forms a Pact with Neku, and while Neku initially dislikes him, they eventually bond over their shared hatred for humanity. As the Game progresses, Neku slowly begins to change his views on people, making Joshua question his own views in turn.

During the week, however, Neku slowly begins to realize that Joshua is the one who killed him. This creates a rift in their relationship, however, on Day 7, it's supposedly revealed that Neku was actually killed by Sho Minamimoto (who was in a shootout with Joshua). At the end of the day, and after their battle with Minamimoto, Joshua supposedly sacrifices himself to protect Neku from Minamimoto, filling Neku with guilt for blaming the other boy for his death and viewing him as a martyr.

On the last day of Week 3, Joshua reveals that he actually survived Minamimoto's attack and that he's the Composer of Shibuya. He also reveals that Minamimoto killing Neku was a lie; Joshua really did shoot Neku to use him as his Proxy for the Game. Joshua then challenges Neku to a duel; if Neku kills Joshua, he'll become the Composer and stop Joshua from destroying himself and Shibuya. However, Neku can't bring himself to Erase Joshua, despite everything he's done and despite knowing that Joshua will destroy the city if he continues being the Composer. Neku values Joshua more than the city of Shibuya, even after Joshua did everything in his power to make Neku hate him.

Because Neku chose to trust Joshua, he decides that Shibuya is worth sparing. Joshua watched Neku change from someone who tried to kill Shiki with very little prompting after only knowing her for a day to someone who had all the reason in the world to kill Joshua but didn't. Neku is also the only person close to Joshua who chose him over Shibuya, as Kitaniji chose to start the Long Game instead of actually try to fix Shibuya while Hanekoma chose to assist Minamimoto in his attempted coup.

After Neku is revived, he says to an absent Joshua that while he doesn't forgive him for everything that happened during the Game, he still trusts him and wants to see him again. While Joshua doesn't accept this request, he watches it from afar. In the secret cutscene (unlocked by getting every Secret Report) Hanekoma notices that Joshua seems sad that he can't join Neku and his friends, and leaves when Hanekoma says it's their world.

Another Day
In the deeply strange alternate universe known as Another Day, Joshua's abrasiveness is tuned down and he becomes much more of a token gay character. The alternate Joshua makes more flirtatious comments towards the alternate Neku. When Neku tries going into the Shibuya River after forming the "Crayon Warriors", Joshua is the first one to willingly go into the River with him. Shiki and Beat will freak out over this, with Shiki even saying that she knew that blue and pink (Neku and Joshua's code names in Another Day) went together but she didn't know that they "went LIKE THAT!" When Neku complains about this reaction to Joshua, he responds with the infamous "Shut up and walk, dear" line.

Fanon
It's a popular ship in the TWEWY fandom, mainly due to the fact that the story's conclusion is about their bond with each other; Neku chooses Joshua over the whole of Shibuya after he stops being misanthropic, while Joshua chooses to spare Shibuya (and as a result, continue living) because he finally had someone who cared about him more than the city in the form of Neku.

Fandom
FAN FICTION