personal history
Maya started out as a member of Checkmate Four: a group of leaders among a race of beings called Fangire. The main diet of Fangire is human life energy: they regard humans as sentient food, though not necessarily as cattle. For reasons unknown, the Fangire don human forms and hide themselves among the human population. This resulted in Fangire falling in love with humans, and Maya, as Checkmate Four's Queen, was an executioner who sought out these "traitors" and killed them.
For centuries, Maya had no qualms about doing this. Then she met Kurenai Otoya.
When she met Otoya, she was already curious about humans, and wanted to find out what drove all the Fangire she executed to love humans more than their own lives. She had discovered and loved music, and Otoya, being an extremely talented violinist and a passionate man, was a fascinating subject. He's also part of an organization that fights and kills human-eating Fangire, so Maya probably thought there was some irony in that.
Hanging out with Otoya garnered the jealousy and ire of Otoya's girlfriend, and somewhere along the line (probably because she wants to monopolize his time), Maya starts scheming to take him away from her. Poor Otoya, who'd fallen in love with both women on first sight, is addled by Maya and just doesn't know what to do. Even after he discovers that Maya is a Fangire, he refuses to kill her. This fascinates Maya even more: it's as irrational as a human-loving Fangire.
Maya, however, is the Fangire Queen. The Bishop (Checkmate Four is comprised of King, Queen, Bishop, and Rook) knows of her dalliances with Otoya and disapproves, especially because Maya is 1) married to the King, and 2) has a kid with him. When the King makes his appearance in the series, it spells trouble. As powerful of a Fangire as Maya is, the King, in comparison, may as well be invincible. And the Fangire hierarchy is ruled by power: the King is literally the strongest Fangire.
The King, as with most Fangire, doesn't recognize love (through their actions, Fangire certainly feel love, but they don't acknowledge it. Possibly because the Fangire as a race are kind of war-like, and marriages seem to always be arranged--presumably for the sake of the species' survival), and thinks Maya should cut it out with this nonsense. Maya gets out of that conversation by saying she's only playing, but it becomes increasingly clear that she's not. While Maya doesn't love the King, he indicates through his actions that he does, in some way, love her. When Maya continues to see Otoya, the King kidnaps and tortures Otoya.
When Maya doesn't move against King or try to rescue Otoya, she is confronted by Yuri, Otoya's girlfriend, who begs Maya to tell her where Otoya is being held, saying that, even if Otoya had betrayed her, she loves him, and would willingly part with her life attempting to rescue him. Maya says that she is silly. But while Yuri is preparing to rumble, Maya shows up, reiterating that Yuri is silly, and goes with her to Castle Dran. There, Maya fights the King while Yuri gets Otoya away. In a not-so-shocking twist, Maya loses, and the King takes away her Fangire-ness.
Maya, without her Fangire-ness, may as well be human now, and utterly powerless in the face of Fangire attacks. Which happens some time later, as Maya was on her way to go see Otoya. She is saved by Yuri. When Yuri has gotten her safely away, Maya repeats what happened to her in some kind of shock, but Yuri doesn't care. In fact, Yuri only saved the woman who stole her man because she brought that man. She'd just broken up with Otoya, and unsmilingly wishes them well because she loves Otoya too much not to.
Before Otoya and Maya can get domestically happy, the King shows up again, threatening Taiga, Maya's and King's son. If she doesn't come back to him, he'll kill Taiga. (See, this is why no one believes he doesn't love her. In a stalkery, dnw kind of way.) Otoya just tells her later that he'll rescue Taiga. This conversation is interrupted by Wataru, Maya's and Otoya's son from the future.
Otoya makes some "from the future?! Are you high, kid?" noises, but Maya believes him. When Otoya goes off to storm Castle Dran, Maya asks Wataru to go help him. Wataru does, and Otoya and Wataru manage to kidnap Taiga. Only not. They are met outside by the King. Wataru drops Taiga off in his mother's arms before he and Otoya go fight the King.
They do manage to kill him, but Otoya had been using a Fangire power artifact for the fight, one that endangers his life. After Wataru returns to the future, Otoya dies.
Wataru is then born, and, some years later, after he has become a little boy, Maya leaves him at Otoya's house and disappears from the boy's life.