Royai

Royai is the het ship between Roy Mustang and Riza Hawkeye from the Fullmetal Alchemist fandom.

Canon
Prior to the events of Fullmetal Alchemist, Roy and Riza met as teenagers while Roy was learning alchemy from Riza's estranged father, Berthold  Hawkeye. Afraid that his research would fall into wrong hands, Berthold Hawkeye tattooed his daughter's back with the secrets of flame alchemy. After Berthold Hawkeye dies of an unknown illness, Roy and Riza visit his headstone. Roy gives Riza his number and Riza, impressed by Roy's dreams, shows him the research so he can leave and finally become a State Alchemist. A little afterwards, Riza also joined the military, following Roy and his naïve idealism. During the Ishval Civil War, both Hawkeye and Mustang were outstanding, earning the names "The Hawk's Eye" and the "Flame Alchemist" respectively. After the war, Riza, terrified of what they did, asks Roy to burn the tattoo off her back so that no one else could have access to her father's research and therefore the deadly damage that Flame Alchemy can do. Reluctantly, Roy agrees, burning the bare minimum.

However, later, after they've both been deployed from the battlefield, Hawkeye decides to join Mustang's team and serves as his bodyguard as well as assistant and trusted confidant. During this scene, Mustang tells Hawkeye to shoot him in the back if he ever strays from his path. Hawkeye agrees, stating, "Of course, I do, sir; I'll follow you into hell if you ask me to."

For much of the anime/manga, Mustang is a colonel in the Amestrian State Military and Hawkeye is his First Lieutenant. Hawkeye serves as Mustang's most trusted confidant, assistant, and even bodyguard. Hawkeye adopts a stern demeanor around Mustang, scolding him often and making sure he does his necessary paperwork.

Later in their military careers, Mustang and Hawkeye were sent to investigate a potential State Alchemist, Edward Elric. Upon arriving at the Elric brothers' home, the two officers discovered that the boys attempted (and failed) the taboo of human transmutation. Mustang and Hawkeye agreed to protect Ed and Al's secret so long as Edward joined the military as a State Alchemist.

As Ed's military superiors, Mustang and Hawkeye keep an eye on the Fullmetal Alchemist and his brother throughout the series. Their protectiveness of the brothers often ropes them into high-stakes situations, including intense battles with supernatural beings. In one such battle, the Homunculus Lust appears to inflict a fatal wound on Mustang.

When Lust tells Hawkeye this, Riza completely loses her cool demeanor that she so often wears. She opens fire on Lust, screaming at her and emptying bullet after bullet into the Homunculus's body as tears well up in her eyes. However, it turns out that Mustang is still alive, and he saves Riza from being killed by Lust. Riza collects herself quickly, reverting back to her normal habit of gently scolding Roy. This situation is reversed later on in the series: this time, Riza is in mortal danger and Roy loses his cool. Riza lies in front of a captured Roy, bleeding out on the ground, and Roy is confronted with a terrible choice in order to save her. Roy struggles against his captors, even screaming, "I'll kill you!" at them as they continue to let Riza bleed. To further agitate Mustang, one of them sneers, "A woman precious to you is dying." Fortunately, Roy is able to reach Riza in time, and he embraces her after her wound is closed.

Near the finale of the series, Mustang is blinded as a consequence of being forced to (unwillingly) perform human transmutation. Hawkeye is upset by this, but stands by his side nonetheless. She proves invaluable to Mustang in the final battle against Father as she directs Roy where to send his flames and gives him positive reinforcement.

The epilogue shows an image of Roy and Riza in the future, still in the military and still devoted to one another.

Fanon
While it's never explicitly stated that Roy and Riza have a romantic interest in each other, there are moments in the manga/anime that suggest that this might be the case. This ambiguity gives Royai shippers the freedom to interpret their relationship in a variety of ways.

Royai fan works often depict Riza and Roy caring for each other on a more intimate level than they are shown to do in canon. Since Riza frequently teases Roy that he's "useless on rainy days" (because water extinguishes his flame alchemy), Royai art and fiction likes to portray the lieutenant tending to a damp and disgruntled Mustang.

Right now, it’s the most written ship for both characters and it’s the most written ship on the Fullmetal Alchemist fandom on AO3.

Fandom
FAN FICTION

FAN ART
 * ロイアイ tag on Pixiv

TUMBLR

Trivia

 * Hiromu Arakawa, the author of Fullmetal Alchemist, was asked by a fan whether or not Roy and Riza got married after the series ended. She replied: "[I] can't get them to marry because of Military Regulations. If they got married, they could no longer stay as superior officer and subordinate." This response could imply that Arakawa thinks of their relationship as romantic.
 * Mustang thinks of his subordinate officers as different chess pieces. He believes that Riza is the "Queen" piece, and even calls her "my Queen."
 * "Ai," seen at the end of "Royai," also means "love/affection" in Japanese.
 * Roy has given Riza permission to shoot him if he ever "strays from the path" and betrays his morals.
 * Roy was mad at Barry The Chopper for having a crush on Riza.
 * Riza tricked Envy into thinking she was in a relationship with Roy for a split second.