"Fly Me to the Moon" centers on the relationship between Nasa Yuzaki, a brilliant but socially awkward young man, and Tsukasa Yuzaki, a mysterious girl who saves his life. The story begins with Nasa, named after the American space agency due to his parents' aspirations, excelling academically but lacking social skills. One night, he encounters Tsukasa after being struck by a truck. Despite his injuries, he is captivated by her beauty and impulsively proposes to her. Tsukasa agrees on the condition that they marry once he graduates high school.

Three years later, Nasa, now living alone, is reunited with Tsukasa, who appears at his doorstep and moves in with him. The narrative explores their evolving relationship as they navigate the challenges of cohabitation and marriage. Tsukasa’s enigmatic background, including her apparent immortality and connection to supernatural elements, adds intrigue to the story. The couple’s interactions are marked by humor, tenderness, and occasional misunderstandings, as they learn to understand each other’s quirks and insecurities.

Supporting characters, such as Nasa’s childhood friend Kaname Arisugawa and Tsukasa’s younger sister Aya, contribute to the dynamic, often providing comedic relief or additional layers to the plot. The series balances slice-of-life moments with supernatural undertones, gradually revealing Tsukasa’s past and the reasons behind her unique abilities. Themes of love, trust, and personal growth are woven throughout, as Nasa and Tsukasa build a life together despite the mysteries surrounding her existence. The story maintains a lighthearted tone while occasionally delving into deeper emotional and fantastical elements, creating a blend of romance, comedy, and fantasy.