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At the start of canon, Alphys and Undyne have a mutual romantic interest in one another but have not yet confessed their feelings. The player's attention is drawn to their UST through offhand remarks in story events (for instance, Alphys mentions her claws shaking when Undyne called her to talk about the weather, then realizes later that there is no weather in the underground and that that cannot be why Undyne actually called her) and optional flavor text (for instance, during Undyne's befriending sequence, she retracts a statement that no nerds are allowed in her bedroom by suggesting that Alphys would be an exception, and keeps soda around for Alphys to drink despite that she dislikes it).
A phone call with Undyne reveals that the two of them met at the garbage dump in Waterfall, and that Undyne called out to Alphys while she was staring into the abyss, implied to be contemplating suicide. She asked Alphys where she thought the pit went, and Alphys told Undyne about all her theories, talking for hours; the two have been friends ever since. In another phone call, Undyne refers to Waterfall as "a great place to meet girls" (appending in another call not to quote her on that).
Their fate is dependent on the player's actions in a Neutral route. If Undyne is killed, she mentions that the knowledge she might die in the line of duty was one of the reasons why she never confessed to Alphys; in any Neutral endings where Undyne dies, Alphys disappears without a trace unless she is the only one left to lead the monsters.
However, the Pacifist route-exclusive events have a greater focus on the two of them, and involve delivering Undyne's confession letter to Alphys. Despite misunderstandings and shenanigans, Alphys is eventually convinced to be open with her feelings towards Undyne and stop trying to act cool around her, and confesses. During the ending of the game the two of them seem to have begun a relationship, and are seen together in the end credits, wearing swimsuits in each other's colors at the beach.
Postcanon materials, such as the Undertale Q&A and the preview for the Undertale Alarm Clock, include mention of the two of them going on hikes together, sometimes accompanied by Asgore. Toby Fox drew attention to a freeze-frame joke from the PlayStation trailer, where Undyne is depicted buying Alphys two box sets of Mew Mew Kissy Cutie 2, unaware that Alphys hates it.
As of December 2017, Alphys/Undyne is the second most popular Undertale ship on AO3 (falling beneath Sans/Reader). On AO3 Ship Stats 2016 it was ranked as the twelfth most popular ship in the Top 20 Femslash section, and for AO3 Ship Stats 2017 it rose four slots to become the eighth most popular ship.
However, fans of the pairing note that the ship is often featured as a background relationship in fanworks focusing more on other pairings or characters. As a solution for readers seeking out works focused on Alphys/Undyne, the additional tag "Alphynecentric" was proposed. The tag is currently wrangled as "Alphys/Undyne-centric" on AO3.
- UNDERTALE ANNIVERSARY - ANIMATED - iscoppie
- alphyneweek on tumblr
- Alphys/Undyne tagged works on AO3
- Alphys/Undyne-centric tagged works on AO3
- Mado's Alphyne Fic Reclist - compiled by madocallie on tumblr (@alphyies on twitter)