In mid-Thirties Hollywood, a new style of funny film blew into fashion. It was as fast-paced and physically raucous as the slapstick that had come before it, but made sophisticated by the shimmering promise of sex, and an unstoppable flow of densely witty dialogue.

Individually, the stars of these films were gorgeous – and when paired off, many of them had the kind of chemistry that could set a cinema on fire. But they weren’t afraid to tumble over a sofa, or drop face-first into the mud, if laughs could be come by in the tumbling.

The menfolk – Cary Grant, Joel McCrea and Clark Gable among them – were dapper, urbane and deeply handsome, which made their pratfalls and comeuppances even more delicious.

But the women were something else. Actresses such as Carole Lombard, Claudette Colbert, Myrna Loy and Irene Dunne had a supernatural flair for this new kind of comedy. Their sex appeal sprang from their wits, verbally and sensually outmanoeuvring their male co-stars – and they had the larger pay cheques to show for it.

Sex was out - except sex can never be out, which meant it had to be dressed up as something else, making it even sexier

At first, the films often looked like battles of the sexes. But in great screwball, sex isn’t all-out war, it’s an uneasy truce. The fun arose from the central couple putting their differences aside and wryly negotiating the swooping zaniness of the outside world together.

The movement was called screwball comedy, after a tricky pitch in baseball that batters found impossible to predict. And the name stuck, because in a good screwball film it’s almost impossible to guess what’s coming next: the only things you can be sure of are that it’ll be fast, and it’ll sting. They combined the best of slapstick, farce and vaudeville with the elegance and eloquence of the romantic comedies made by Ernst Lubitsch in the late Twenties and early Thirties – and even today, the recipe remains largely unchanged.

She’s Funny That Way, the new film from Peter Bogdanovich, is a rare example of a modern screwball comedy – but the pleasure it takes in showing beautiful people (Jennifer Aniston, Owen Wilson and Imogen Poots) turning life into a crazy adventure is of a Thirties vintage. With those ingredients, screwball should have been the most popular idea in cinema history. And for a few years, at least, it was.

At the Academy Awards in 1935, It Happened One Night – a blissful odd-couple caper in which Gable’s rakish journalist joins Colbert’s absconded heiress on a trans-American road trip – made a clean sweep of the so-called Big Five categories, winning Best Picture, Best Actor, Best Actress, Best Director (for Frank Capra) and Best Screenplay. But less than a decade later, the genre was all but burnt out, and only sporadic attempts have since been made to revive it.

Clark Gable and Claudette Colbert in 'It Happened One Night' Credit: Everett Collection / Rex Features

So who killed screwball comedy? And after being left to moulder for the best part of a century, can the body be resuscitated?

To get to the bottom of screwball’s untimely death, you have first to understand the conditions under which it flourished. The Great Depression bit in 1929, and people looked to cheap, glamorous cinema for an escape route. But at the same time, the moral codes governing film production were tightening, with the Catholic Church and the League of Decency both deeply concerned about exactly where it was all these cinemagoers were escaping to.

Sex was out – except sex can never be out, which meant it had to be dressed up as something else, which in turn made it even sexier. “The sanctity of marriage and the home shall be upheld,” boomed the Motion Picture Production Code in 1930. In practice, this meant films that wanted to show romance out of wedlock had to start with a married couple and split them up, then allow them to philander with other suitors, and bring them back together for a happy – and technically morally upstanding – ending.

In Leo McCarey’s The Awful Truth (1937), Dunne and Grant play Lucy and Jerry Warriner, a high society couple whose doubts over each other’s fidelity bring about a divorce. The split is amicable enough, except for who gets custody of the dog (screwball comedies seldom involve children: they raise the stakes in the wrong way), but when they start seeing other people, they realise they were made for one another. Jerry, a debonair and worldly-wise Manhattanite, goes out of his way to sabotage Lucy’s relationship with Ralph Bellamy’s docile Oklahoma oilman, whose immeasurable wealth doesn’t quite make up for the fact that, well, he’s no Cary Grant.

Later in the film, Lucy more than returns the favour, destroying Jerry’s engagement to a society heiress with one of the funniest scenes in the screwball cycle, and hence cinema in general. (She pretends to be his sister. There’s feigned drunkenness. Then she sings a song. It’s perfect.) Grant’s face during all this sums up the screwball hero’s plight: he’s been exquisitely humiliated by his other half, and he loves it.

Irene Dunne and Cary Grant in 'The Awful Truth' Credit: Everett/REX Shutterstock

One crucial reason screwball caught on in the thick of the Depression is that its charades remained just that. It Happened One Night was honest about the world being in disarray: the story takes place on night buses and campsites, among displaced people.

Though the idle rich were stock screwball characters, they were objects of fascination, not aspiration. “That’s the tragedy of the rich – they don’t need anything,” Charles Coburn’s card sharp observes in Preston Sturges’s The Lady Eve (1941), shortly before taking Henry Fonda’s explorer for $32,000 in a game of double-or-nothing. Screwball heroes were allowed to be rich, but only if they were fooling someone richer.

These were the conditions under which screwball thrived – and in 1934, it looked as if it had taken root. It Happened One Night triumphed at the box office, while Carole Lombard showed that a movie star could be beautiful and funny at once in Howard Hawks’s Twentieth Century, playing a lingerie model-turned-Broadway star.

But it couldn’t last. As America marched towards the Second World War, screwball was drowned out by proudly harmless comedy serials, such as Mickey Rooney’s Andy Hardy films, which charmed mass audiences without playing cat-and-mouse with the Production Code.

Screwball’s dominant women also fell from fashion – or rather they slipped off down a smoky alley and into film noir, where they morphed into the femme fatale. Male double-acts such as Abbott and Costello, and Crosby and Hope, came back to comedy, and patriarchy quietly reasserted its grip.

Given our current social climate, though – with the prevailing appetite for strong female characters, keen awareness of inequality, and growing wariness over what can and can’t be said – it may be time for screwball comedy to make a comeback.

Jennifer Aniston and Rhys Ifans in 'She's Funny That Way'

Though few recent films qualify as out-and-out screwball, some memorable ones are kindred spirits. While Brad Pitt flits excitedly from phone call to phone call in Bennett Miller’s Moneyball (2011), you can see the spirit of Rosalind Russell in His Girl Friday (1940) working through him – and Amy Adams seducing Bradley Cooper with a fake English accent in David O Russell’s American Hustle (2013) is Barbara Stanwyck in The Lady Eve all over again.

And then there is Bogdanovich, who turned the defibrillators on screwball once before in 1972’s joyous What’s Up, Doc?, with Barbra Streisand and Ryan O’Neal – and whose new film, set in the ego-littered world of Broadway theatre, could almost be a 21st-century remake of Twentieth Century.

Among the many good things in She’s Funny That Way is Aniston’s performance as a venomous therapist, which is the best thing she’s done in years. She’s an actress whose talents are perfectly suited to screwball, although her post-Friends career has rarely allowed her to show it. It has taken a director of Bogdanovich’s shrewdness to spot this, and give her a role that allows her to let rip.

It makes you wonder what a different career Aniston might have had if she’d been a star in the Thirties. Would she have been riffing through the sound barrier with Grant and Gable? Vying with Colbert and Lombard for box-office supremacy?

It’s certainly a thought – and not as screwy as it might first appear.

She’s Funny That Way is released in cinemas on June 26