At a time when gender seems increasingly to reside more in the soul than in the body, a movie like “The Danish Girl” can be tricky to talk about.

Before its release, critics received a guide to currently acceptable terminology such as “transgender,” meaning those who do not identify with their biological sex, and “cisgender,” meaning those who do. “The Danish Girl,” then, is the true story of Einar Wegener (Eddie Redmayne), a Danish artist who was born biologically male and underwent sex-reassignment surgery in the early 1930s — a risky decision for many reasons. Alicia Vikander plays Einar’s cisgender wife, Gerda, who stayed by Einar’s side through her transition to Lili Elbe.

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Lovely-looking, beautifully acted and a bit problematic,the film is directed by Tom Hooper, the Oscar-winner behind “The King’s Speech.” In that film, a stuttering king overcame his social stigma; in this film, Lili must embrace hers. “The Danish Girl” looks to history to help us understand a kind of identity that only seems new, thanks to suddenly high-profile transgender people like Caitlyn Jenner.

“The Danish Girl”is set in a time when people like Einar were virtually unheard of even among bohemians and freethinkers (Amber Heard is delightful as Ulla, a saucy libertine). Homosexuals — that’s the film’s term — didn’t quite know what to do with this masculine figure in a dress, while doctors leaned toward forcible institutionalization. Redmayne brings great sensitivity to the role of a happily married artist whose male façade is crumbling. Lili must emerge, even at the cost of Gerda’s happiness.

Written by Lucinda Coxon from David Ebershoff’s 2000 novel, “The Danish Girl” has an odd habit of fetishizing Einar’s femininity. It seems constructed largely of an erotic attraction to taffeta and silk. When Einar becomes Lili (her surgeon is played by a no-nonsense Sebastian Koch), she abandons art to become a giggling shopgirl. If this was indeed the real Lili, then so be it — but there’s something reductive in the way Lili is presented.

In the end, the film’s most eloquent character is Vikander’s brave and very moving Gerda. It’s she who makes the case that gender does not define a person. Maybe Gerda was married to Einar, maybe to Lili all along, she says. “But really, it was you and me.”