Coppélia is one of the sillier corners of the ballet repertoire. Franz, a handsome young villager, spies his perfect woman and instantly falls in love, and his fiancee Swanilda flips out. When the "other woman" turns out to be a life-sized doll, everyone has a good laugh about it and lives happily ever after.

Erina Takahashi, who'll be dancing the part of the doll in English National Ballet's upcoming production, says it is "such fun to do". But this is a story with dark undertones. The dollmaker, Dr Coppelius, attempts to sacrifice Franz in order to bring his creation to life, and the ballet's source material, ETA Hoffmann's short story The Sandman, features a sinister eye‑stealing alchemist.

Coppélia was one of a wave of 19th‑century works that featured almost-human protagonists, from Frankenstein and Pinocchio to Champfleury's Wax Figure Collector. But the idea of the model coming to life, particularly as an object of desire, stretches back to Greek mythology and Pygmalion, who carved a statue so realistic he fell in love with it. And that idea endures.

Let's not forget Kim Cattrall's finest moment in Mannequin, as the shop dummy brought to life to the sound of Starship's Nothing's Gonna Stop Us Now. There's Fellini's Casanova, in which a mechanical doll, Rosalba, trumps all the great lover's women. And Buffy the Vampire Slayer's Buffybot, created by three nerdy wannabe supervillains who can't get girlfriends.

There's a whole subset of inanimate dolls in visual arts, from Hans Bellmer to the Chapman Brothers, mostly of an unnervingly sexual bent. And in recent years the theme has popped up again in various guises, whether in the surprisingly sweet Ryan Gosling film Lars and the Real Girl (deluded loner buys a sex doll to be his girlfriend), Ruby Sparks (frustrated author writes his perfect woman, who then materialises in the flesh), or Spike Jonze's Her, where the automaton doesn't even need a body since she's got Scarlett Johansson's voice. It's all the same fantasy.

Last year, artist Pauline Bewick and composer Raymond Dean collaborated on an opera, The Alma Fetish, based on a true story Bewick had become fascinated by. In the 1910s, Austrian artist Oskar Kokoschka fell madly in love with Alma Mahler, widow of composer Gustav. When Mahler ended their affair, a distraught Kokoschka ordered a life-sized doll to be made in her image, complete with silk thighs. He took it to parties and to the opera, but ultimately the charm wore off. "When dawn broke – I was quite drunk, as was everyone else – I beheaded it out in the garden and broke a bottle of red wine over its head," Kokoschka wrote.

Ironically, as we make inanimate things more human – whether it's round-eyed Pepper the robot, who can read emotions, or a child's baby doll with a floppy head and bodily functions – there's a roaring trade in making ourselves look more artificial, with Botox, breast implants, fake hair and HD-ready makeup. The real/fake confusion spills into art, in Jeff Koons's sculpted album cover for Lady Gaga, in the human Barbie-doll portraits of Alex Sandwell Kliszynski or American artist Amber Hawk Swanson, who married her own lookalike doll in Vegas.

So what is the enduring appeal of the not-quite-human? Of the beautiful creation come to life? There's sex, of course. The lonely man who can't get a real woman and gets a RealDoll instead (don't Google that in polite company). But according to Marquard Smith, author of The Erotic Doll: a Modern Fetish, it's much more about playing God. "For time immemorial we've been interested in making things in our own image, or making things we want and desire," says Smith. "It's narcissism. We have an elevated sense of our species and how the most incredible thing we could do would be to make ourselves. It's about us being at the centre of the universe and dictating the world."

Being human, after all, brings with it a raft of unwanted side effects. We might wield our power over matter, but there are plenty of things we can't control – you can't make someone fall in love with you.

"There's an issue with fear of rejection and a need to retain power and feel safe," says psychologist Jemma Tosh of the allure of the inanimate lover. There's even a word for it, agalmatophilia. "Having an object removes the complications," says Tosh. But it's not as weird as you'd think, she insists. All sorts of objects become loaded with sensual meaning – women's lingerie, for example, when there's nothing inherently sexual about lace. "A doll is taking it to a different level, but it's a continuum of the same thing. When we think of an object in that way it becomes less 'odd'."

There are plenty of objects we love, in lustful or sentimental ways, whether shoes, handbags, teddy bears or old photo albums. Despite what the era of downloads and ebooks might tell us, touch and tactility are important, says Smith. "I mean, I love my iPhone much more than I love anyone I might be talking to on it," he says, possibly exaggerating a little. "That's because I spend so much time touching it, stroking it, scrolling, and oh … it just buzzed in my ear, which is quite exciting."

Many of these stories aren't about sex so much as acting out difficult emotions. In Lars and the Real Girl, Lars uses his "girlfriend" Bianca to work through paralysing emotional issues. For Joaquin Phoenix's character in Her, Sam is the rebound fling that helps him get through his divorce. And Oskar Kokoschka's artificial Alma was a very vivid way of living out his grief at being rejected.

You can't help notice the gender representations are somewhat skewed. What do women do with their problematic feelings and desires? They probably talk to their friends about them, or, in EL James's case, turn them into a bestselling book. The fact is, female desires are all out in the open.

But that's not to say we don't have a use for a doll. In 2000, Suzanne Heintz got so sick of her mother asking when she was going to get married and have children, she bought a ready-made fibreglass family from a mannequin sale and posed them for a series of photos satirising society's expectations of women.

Heintz has been through a lot for her fake family. She's been considered a terror threat, forbidden from buying seats for them on aircraft and banned from public transport. She's taken them skiing, ice skating, to dance lessons (with her "husband" Chauncey mounted on a skateboard) and on a dogsled ride in the Rockies. "It's all fantastically ridiculous," she says. "But so is living your life going through the motions because 'that's just what people do'."

Heintz recently staged a wedding to Chauncey in Colorado, with her real‑life boyfriend as the best man. After 14 years, has she become attached to her automatons? Was it emotional? "No," says Heintz. "I ended up leaving him at the altar."

• English National Ballet's Coppélia is at the London Coliseum, 23-27 July, and tours in the autumn. Details: ballet.org.uk