We often talk about how stars can disappear beneath makeup and prosthetics and padding and wardrobe, to the point where they’re virtually unrecognizable.

If nobody told you who was playing Dick Cheney in “Vice,” would you have guessed Christian Bale? What about Gary Oldman as Winston Churchill in “Darkest Hour,” or Tilda Swinton playing an old man in “Suspiria,” or even Margot Robbie in “The Favourite”?

For the sweet-natured, occasionally melancholy and thoroughly entertaining Hollywood biopic “Stan & Ollie,” John C. Reilly reportedly spent four hours in the makeup chair every morning to transform himself into Oliver Hardy, and no doubt Steve Coogan had to allocate more than a few minutes every day to achieve resemblance to Stan Laurel — but in both cases, they don’t disappear so much as they seem to meld with their subjects.

Which makes the work all the more endearing and authentic.

Directed by Jon S. Baird and written by Jeff Pope, “Stan and Ollie” is a brisk (97 minutes), meticulously staged, no frills, almost too conventional “two-hander” focusing primarily on the legendary comedic duo’s 1953 tour of the United Kingdom, some two decades past their peak years.

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First, we spend a little time in the mid-1930s, when Laurel and Hardy were a wildly popular duo, churning out hit after hit for the Hal Roach Studios. (Danny Huston, a third-generation Hollywood mainstay himself — half-brother of Angelica, grandson of Walter — is terrific as the no-nonsense Roach).

In a sense, Reilly and Coogan are playing dual roles: the hapless, hilarious, slapstick duo in front of the camera, and the men playing those well-honed characters.

When they’re “on,” Laurel is the bumbling, stumbling goofball, and Hardy is the pompous foil who constantly finds himself the butt of the joke. In real life, so to speak, Laurel is the more cerebral and ambitious and business-minded of the two, while Hardy is a bit of a dreamer with a weakness for betting on the ponies.

Ah, but what a team they make! Magic in front of the camera, friends and partners after the director barks “Cut!”

Flash forward to Newcastle, England, 1953, with Laurel and Hardy arriving at the decidedly downscale Bottle & Glass Inn. (And just in case we don’t get the message about their current lot, it literally begins to rain on the fellas.)

The boys — who are now late middle-aged men — are embarking on a tour of mid-level music halls, carnivals, diners and beauty pageants while Stan secures financing for their cinematic comeback.

Onstage, they still have the magic touch — but Oliver is not well, and he huffs and puffs and sweats profusely from the physicality required of their routines, while Stan can barely disguise the sadness he feels when he’s reminded younger audiences don’t even know Laurel and Hardy were once the greatest and most heralded comedy duo in the world.

Shirley Henderson adds spice as Lucille Hardy and Nina Arianda is a deadpan delight as Ida Laurel, the long-suffering but loving wives. (More accurately, the LAST of their respective wives. Laurel was married four times; Hardy thrice.) As long-simmering differences between the old partners reach the boiling point and they reach a serious impasse, it’s the wives who provide the humanity and, in some cases, the much-needed humor.

“I loved us,” says Stan.

“You loved Laurel and Hardy, but you never loved ME,” replies Oliver.

“So what?” says Stan.

Tough stuff — but we get the feeling these two giants of comedy will work through the disappointments and the missed opportunities, the perceived acts of betrayal, the bruised egos, all of it.

After all, theirs was a marriage of sorts as well, a partnership that created some timeless comedy and influenced generations of performers. Thanks to the subtle brilliance of Reilly and Coogan, even someone who’s never heard of Laurel and Hardy would likely see how magical these two were together.

‘Stan and Ollie’

★★★

Sony Pictures Classics presents a film directed by Jon S. Baird and written by Jeff Pope. Rated PG (for some language, and for smoking). Running time: 97 minutes. Opens Friday at local theaters.