He shared a bath with Laurence Olivier (Spartacus), a bed with Janet Leigh (the first of his six wives) and was one half of a flamboyant 70s crime-fighting duo with Roger Moore in The Persuaders. But despite his luxuriant locks and matinée idol looks, Tony Curtis, is best remembered for embracing his feminine side as a cross-dressing musician in Billy Wilder’s Some Like It Hot (1959).

Curtis, who came to acting via a stint in the US Navy, was born Bernard Schwartz in the Bronx on 3 June 1925. He was under contract to Universal from the late 40s, and one of his earliest roles was opposite his future wife, Leigh, in Jerry Lewis’s bizarrely-named short, How to Smuggle a Hernia Across the Border. I suspect not too many people remember that one, but he played the title roles in Houdini and Son of Ali Baba in the early 50s, before being (mis)credited with that line “Yondah lies the castle of my faddah” in 1954’s The Black Shield of Falworth.

In 1957, Curtis gave one of his greatest performances in the ironically titled Sweet Smell of Success. Directed by Alexander Mackendrick from a screenplay by Clifford Odets and Ernest Lehman, it was a box-office failure. This cynical tale of scheming press agent Sidney Falco (Curtis) and his attempts to curry favour with big-shot Broadway columnist JJ Hunsecker (Burt Lancaster) was probably ahead of its time. It dared to shine a light on the sordid and self-serving world of celebrity journalism and, as Lancaster’s biographer Kate Buford puts it, “drowned in a river of red ink and popular repugnance”.

As Falco, Curtis is the consummate liar and the ultimate wheeler-dealer — a man made for the night and the city, which in this case is New York. He lives in his office and treats women with a barely disguised contempt. Lancaster, whose production company made the film, has the kind of commanding screen presence that can make his co-stars look insignificant. It’s a tribute to Curtis that his restless, ruthless and oleaginous Falco holds his own against the eerily calm Hunsecker. One of the film’s most famous lines is “Match me, Sidney” – Curtis certainly does that.

Sadly, he didn’t get an Oscar nomination then, or for his part in cinema’s most famous cross-dressing comedy, Some Like It Hot. It’s one of those films that you watch repeatedly, but I must admit to being more a fan of Curtis’s coolly authoritative and rather sultry Joe/Josephine, than Jack Lemmon’s shrill Jerry/Daphne. Of course, everyone remembers Curtis’s rather ungallant “kissing Hitler” comment in reference to his scenes with co-star Marilyn Monroe. He later claimed it was a “joke” answer to a “darn stupid” question, but given Monroe’s reputation as one of cinema’s tragic victims, it doesn’t reflect well on Curtis.

Curtis’s production company, Curtleigh, made just four films including Sweet Smell, The Defiant Ones (for which he was Oscar nominated) and the preposterous The Vikings, co-starring a one-eyed Kirk Douglas. Perhaps if he’d originated more of his own projects, Curtis would have rivalled the success of Douglas, whose company Bryna made the Oscar-winning Spartacus in 1960.

I find the notorious and innuendo-laden “snails and oysters” scene in Spartacus with Curtis and Olivier very silly. Its restoration seems like more of a gift to comedy than posterity. For me, the most affecting and schmaltz-free sequence is the fight to the death between brothers in arms Spartacus (Douglas) and Antoninus (Curtis). To the “victor” goes the prize of a slow death.

The Boston Strangler (1968), in which Curtis stars as real-life killer Albert DeSalvo, is one of those overlooked films from an underrated director (Richard Fleischer) that rarely turns up on TV. Apparently, the actor considered it one of his favourite movies and also ranked it among his most challenging roles. Some found the depiction of the murders here too lurid, but any lingering doubts that Curtis was just a pretty boy – a cinematic lightweight – are dispelled by his graphic re-enactment of his crimes in the presence of investigator Henry Fonda.

If the extensive list of “personal quotes” on IMDb is anything to go by, Curtis was something of a raconteur, as well as a ladies’ man, an accomplished painter and, of course, father to Jamie Lee Curtis. He worked intermittently over the past decade, and his final completed film was David & Fatima (2008). Perhaps he didn’t quite scale the heights of contemporaries like Paul Newman and Marlon Brando, but his lengthy filmography contains a few real gems and film fans will always cherish that Cary Grant impersonation from Some Like It Hot.