AsuShin

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

Canon
As Neon Genesis Evangelion is meant as a deconstruction of anime tropes, so is Asuka and Shinji's relationship a darker take on tsundere 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, as Asuka remains jealous of his abilities and disgusted by his weaknesses. In Episode 15, they kiss, but their relationship only becomes distant from then out. The tensions between the two grow and they are unable to continue fighting together effectively.

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 and her jealously towards him. Likewise, Shinji is unsure of how to reach out to her, and fails to understand her hints. 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 throws 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" "Ambivalence"  "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 angrily blames Shinji when his syncronization with Rei causes Asuka to cry. She orders him to comfort Asuka, which he does.
 * Asuka declares her room door "the impenetrable wall of Jericho", a hint that she hopes Shinji will come and support her.
 * When half-asleep, Asuka falls into Shinji's bed. Shinji tries to kiss her, 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 ends poorly.
 * 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, though she tries to hide herself. Shinji laughs for the first and only time because of this.
 * Toji calls Asuka and Shinji "quarreling newly-weds". The pair has double-blush and makes the denial in perfect sync.
 * Hikari notes that Asuka and Shinji always walk home together, and apologizes when she asks Asuka to walk with her instead. This suggests again that Hikari sees Asuka and Shinji as a couple.
 * Kaji has been encouraging Asuka to reach out to Shinji since before the two properly met.
 * Shinji tries to talk with Asuka and find out more about her family.
 * Asuka seems jealous when she notices Shinji and Rei talking together.
 * 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, in an apparent attempt to comfort her.
 * Shinji monologues that he wishes he knew where Asuka was, and that he wants to talk to her again.
 * In a reality that evidentally 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 tells Asuka he wants to help and stay with her.
 * Asuka strokes Shinji's face when he strangles her, causing him to break down in tears on her chest.

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 and accept their feelings. Those who prefer other pairings, especially those who felt uncomfortable with the aggression in 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 should or will end up with in the Rebuild movies.