The story takes place in 1920s Denmark. Greta* was a portrait painter, and needed a model. She asked Einar to step into a dress, stockings, and heels, and created some kind of awakening in Einar. In women's clothes, her husband became an outrageous character named Lili. The paintings of Lili became extremely popular, few realizing a man had stood in for them. Lili than took on a public life of her own, and Greta often introduced Lili as her sister. Eventually, Einar / Lili decided to commit to gender reassignment surgery, a dangerous and experimental procedure at the time. Greta stood beside her husband until his transformation was complete, and then their marriage was declared null and void by the King of Denmark.
I'm anxious to see Alfredson tackle the material. The real question is how Kidman will play Lili and Einar without making it seem like a joke. The real Einar reportedly had very feminine features before his surgery, so it's within the realm of believability. But I love that she's willing to try. Sneering at Kidman seems very popular these days, and it's a shame, as there are few actresses willing to take the risks she is, for better or worse.
*It's spelled Gerda historically, I'm not sure why they're changing it here.