On an alternate Earth, an alien force called the Neuroi has overrun the skies, and ordinary weapons do nothing against it. The world's militaries instead deploy Witches: young girls who manifest animal ears and tails when they channel magic and strap on Striker Units, leg-mounted machines modeled on real fighter aircraft. Yoshika Miyafuji, a healer's daughter from the Fuso Empire, joins the international 501st Joint Fighter Wing partly to learn what became of her father, training alongside veterans like Mio Sakamoto.