AsuShin

AsuShin is the het ship between Asuka Langley Soryu and Shinji Ikari from Neon Genesis Evangelion.

Canon
As Neon Genesis Evangelion is meant as a deconstruction of anime, so is Asuka and Shinji's relationship a deconstruction of tsundere anime romance stories.

Asuka and Shinji meet in Episode 8, "Asuka Strikes". Although Asuka finds Shinji to be boring and overly passive, she quickly comes to respect his piloting ability and the two become friendly rivals. Asuka moves in with Shinji and Misato in Episode 9, as the adults note their potential for piloting together. Their relationship grows as the show progresses, albeit subtly. In Episode 15, they kiss, but their relationship only becomes frosty from then out. The tensions between the two grow and they are unable to synchronize their fighting.

In Episode 22, it is confirmed that Asuka has been wanting Shinji's affections, but is too afraid to communicate herself directly to him. Asuka is terrified of being rejected, and simultaneously conflicted by having feelings for Shinji despite his flaws. Shinji fails to notice her hints, which drives Asuka away. Likewise, Shinji is unsure of how to reach out to her. Towards the end of the series, Shinji increasingly tries to connect with her, but he finds her aggressive nature and constant mixed messages to be scary and confusing.

By the End of Evangelion, Shinji is throwing himself at Asuka, looking for support. Though Asuka is left comatose after a suicide attempt, Shinji is repulsed by Rei and Misato, and distraught by Kaworu's death. In a surreal and unclear scene, Asuka callously and violently rejects Shinji. Whether real or a product of his own self-loathing, this acts as the final straw in Shinji's decision to trigger the Third Impact and wipe out humanity. Shinji ultimately has a change of heart, but not before the world is all but destroyed.

In the final scene of the show, Asuka and Shinji are alone in the post-apocalyptic wasteland. For unknown reasons, Shinji strangles her, but stops when she strokes his cheek. Their relationship is left on an inconclusive note. While they are together, and with implications that Asuka has come to accept her feelings for Shinji, they are also the only apparent survivors, with even further trauma from the horrors of their experiences.

Moments
"Both of You, Dance Like You Want to Win" "Magma Diver" "The Day Tokyo-3 Stood Still" "Those Women Longed for the Touch of Other's Lips, and Thus Invited Their Kisses" "Splitting of the Breast" "Fourth Children" "Don't be" "The Beginning and the End, or 'Knockin' on Heaven's Door'" "Take Care of Yourself"  "Love is Destructive" "I Need You"
 * Hikari tells Shinji to comfort Asuka when Misato and Rei make her cry.
 * Asuka declares her room door "the impenetrable wall of Jericho", a hint that she hopes Shinji will come and support her.
 * Shinji tries to kiss Asuka in her sleep, which she finds out about the next day.
 * The two of them defeat the Angel in perfect synchronization.
 * Asuka flirts with Shinji by helping him with his homework, drawing attention to her breasts, and showing off her diving skills.
 * Shinji dives into a volcano to save Asuka. Asuka smiles at this.
 * Asuka tries to comfort Shinji after his call with Gendo.
 * Asuka returns Shinji's favor in the previous episode by putting herself in danger to protect him.
 * Asuka compliments Shinji on his cello skills.
 * Shinji and Asuka kiss, though Asuka pretends it is only out of boredom. We learn in Episode 22 she was trying to reach out to Shinji for support.
 * Asuka encourages Shinji to take the lead against the Angel, which Shinji does.
 * Asuka visits Shinji in the hospital. Shinji laughs for the first and only time because of this.
 * Toji calls Asuka and Shinji "quarreling newly weds". Que double-blush and denial in perfect sync.
 * Kaji has been encouraging Asuka to reach out to Shinji since before the two properly met.
 * Shinji is curious about Asuka's family life.
 * The Angel forces Asuka to confront that she has feelings for Shinji despite his apparent rejection of her.
 * Shinji tells Asuka he's glad she's ok.
 * Shinji monologues that he wishes he knew where Asuka was and that he wants to talk to her again.
 * In a reality that reflects what Shinji wishes his life could be, Asuka is his closest friend and apparent love interest.
 * Shinji makes clear that he is afraid of Misato and Rei, and any desire he may have had for them is gone. He only wants Asuka.
 * The pairing's most infamous scene: Shinji begs a comatose Asuka to wake up and help him. When he accidentally exposes her breasts, he masturbates to them.
 * Shinji continues to wish that Asuka would protect and help him.
 * Asuka strokes Shinji's face when he strangles her, causing him to break down in tears on her chest.
 * They are the only two people shown to be alive at the end.

Fanon
The dysfunctional and largely destructive nature of Asuka and Shinji's relationship has created a great deal of controversy. Fans of the pairing argue that the two have immense potential as a couple, if they can grow past some of their issues. Those who prefer other pairings, especially those who felt uncomfortable with Asuka and Shinji's dynamic, typically try to argue that the pairing is abusive. Some additionally try to claim that Shinji's attraction to Asuka was purely sexual.

Possibly in response, further installments and spin-offs in the franchise have put additional emphasis on Shinji's relationship with Rei and Kaworu. While Shinji and Asuka are still given romantic scenes, the rival pairings are put on a more equal footing. As a result, the franchise has garnered a reputation as a harem that was not quite accurate for the original show. The fandom still has a very active shipping war, with the main focus being on who Shinji will end up with in the Rebuild movies.