The story begins on the 75th birthday of identical twin sisters, Dora and Nora Chance. By what Dora, who is also the narrator of the story, describes as a bizarre coincidence, it is also the 100th birthday of their natural father, Melchior Hazard, and his fraternal twin brother, Peregrine Hazard, who is believed to be dead. The date is similarly Shakespeare's supposed birthday – 23 April.
Dora and Nora's birthday gets off to a dramatic start when their half-brother, Tristram Hazard, who believes himself to be the nephew of the twins, arrives on their doorstep. He announces that Tiffany – his partner, and the goddaughter of the twins, is missing. Dora and Nora soon discover that Tiffany is pregnant with Tristram's baby, but he is unwilling to take on the responsibility. Once this bombshell has been dropped, it soon emerges that a body has been found, and it is believed to be Tiffany's.
Most of the novel consists of Dora's memories. As well as providing the backstory of her natural father, Melchior Hazard, her legal father, Peregrine Hazard, and her guardian, Grandma Chance, Dora describes key events of her life. These include her early theatre performances, how she and her sister deal with being rejected by their father, as well as the time that she spent in Hollywood, producing a film version of A Midsummer Night's Dream. It also makes the reader wonder about a sexual and incestuous relationship between Peregrine and Dora as there are hints that some sexual activity took place on the Brighton trip, but Carter does not clear this mystery up.
Dora and Nora attend Melchior's 100th birthday party, where he acknowledges they are his children for the first time in their lives. The twins learn that both Peregrine and Tiffany are alive, and the true nature of their long-time enemies, Saskia and Imogen, is revealed.
The novel ends with Dora and Nora being presented with twin babies to look after – a gift from Peregrine. They realise that they "can't afford" to die for another twenty years, as they want to see the children grow up. The final line of the story is a message constantly conveyed by Carter throughout the novel: "What a joy it is to dance and sing!"