“John Garfield should be doing this part, not me.”

This declaration of self-doubt was muttered by a scruffy, largely untried 23-year-old actor at the first table read for a new work by a fast-rising young American playwright. The year was 1947; the setting, a rooftop rehearsal space on West 42nd Street; and the play, after some vacillation on what the title should be, “A Streetcar Named Desire.” Its author: Tennessee Williams.

As for that seemingly unsure young actor, who had heard that his role had already been refused by the go-to working-class film favorite John Garfield? His name was Marlon Brando. His raw, eloquently inarticulate subsequent portrayal of a sexually magnetic blue-collar lout named Stanley Kowalski — the role he was reading that day — would not only make him a star but also help to change the very nature of American acting.

Brando may have once felt he was trapped in the brooding shadow of Garfield. But that was nothing compared to the shadow Brando’s performance — captured for eternity in the 1951 film adaptation of “Streetcar,” which, like the play, was directed by Elia Kazan — would cast over every actor who dared to portray Stanley Kowalski in the years to come.

The latest of this courageous breed is Paul Mescal, who has donned Stanley’s historic T-shirt for the director Rebecca Frecknall’s London-born production of “Streetcar,” which runs through April 6 at the Brooklyn Academy of Music. Initially, some doubts were expressed among star watchers about the casting of Mescal, who had become an international heartthrob after he appeared in the television adaptation of Sally Rooney’s “Normal People.” Wasn’t he too sensitive, too slender, too young to play Stanley? (Never mind that he was in fact a bit older than Brando had been on Broadway.)

But when this latest “Streetcar” opened in London, critics heaved a gratified sigh of relief. The interpretation by Frecknall, known for her high-concept approaches to classics (including the “Cabaret” now on Broadway), was unorthodox but persuasive, they said. So was the casting of Patsy Ferran, a last-minute substitute for an injured actress, as the play’s heroine, Blanche DuBois, whose fragile illusions are crushed by Stanley, her brutish brother-in-law. The general reaction to Mescal was summed up by Andrzej Lukowski’s review in London’s Time Out: “He’s good! Actually very good. (Also: stacked.)” (While admiring the play’s stars, Jesse Green in his New York Times review, was less enthused about the production in Brooklyn.)

Surely, no American drama is as haunted by ghosts of actors past as “Streetcar.” By that I mean not only Brando, but also Vivien Leigh in the film as Blanche (a part originated onstage by Jessica Tandy). Leigh’s interpretation was described by Pauline Kael as “one of those rare performances that can truly be said to evoke pity and terror.”

By the way, the image of Brando, in his torn T-shirt, caterwauling “Stellllla!” (the name of Stanley’s wife), may have become a meme before there were memes. But it’s the Blanches who have generally received the bulk of praise and analysis from critics. In Brooks Atkinson’s 1947 review in The Times, it was Tandy to whom he devoted a long paragraph of lyric description. (Brando was cited as one of three cast members who “act not only with color and style but with insight.”)

It was Tandy who won a Tony Award the next year, while Brando wasn’t even nominated. Leigh, but not Brando, won an Oscar for the movie.

Though “Streetcar” is regarded by many (including me) as the greatest of all American dramas, revivals of it were scant for several decades, perhaps because of the film’s continuing hold on the public imagination. (There were two very brief engagements at New York City Center in the 1950s.) Then in 1973, “Streetcar” received a Broadway revival, starring Rosemary Harris and James Farentino, that reminded New York audiences of its uncommon craft and power. After that, new productions arrived quickly, with a shining assortment of stars enacting the war between Blanche, the fluttering fantasist, and Stanley, the harsh pragmatist, in a shabby New Orleans apartment with their ever-shifting balances of power, between both the characters and the performers.

What follows is an annotated list of some of the Blanches and Stanleys who gave life to what Williams, in a letter to his agent before the play opened, described as “a tragedy of misunderstandings.”

Los Angeles, 1973

Faye Dunaway and Jon Voight

Dunaway was said to be an unusually glamorous Blanche, but also “riveting, original” and unexpectedly funny, Stephen Farber wrote in The Times. Her co-star got off less easily: “To imitate Brando would be hopeless, but Voight’s studious attempt to underplay the role is almost as disastrous.”

Broadway, 1988

Blythe Danner and Aidan Quinn

Though The Times’s Frank Rich felt Danner should have been a natural for Blanche, he wrote that she lapsed all too often into a “fey eccentricity” more appropriate to Noël Coward. He added that Danner and Quinn, “both erotic figures in other circumstances, shed no sparks here.”

Broadway, 1992

Jessica Lange and Alec Baldwin

In this case, it was Kowalski triumphant, according to Rich, who wrote of Baldwin, “His Stanley is the first I’ve seen that doesn’t leave one longing for Mr. Brando,” while filling the play with “the America of big-shouldered urban industrialism.” Of Lange, Rich wrote, “The real problem with her Blanche is less a matter of deficient stage experience than emotional timidity.”

In the first “Streetcar” I reviewed for The Times, the theatrical demolitionist Ivo van Hove set much of his experimental take on the play in a bathtub. Everyone got naked, everyone got drenched — presumably with the aim of stripping away poses and pretensions. McKenzie’s “scrawny, charisma-free” Stanley didn’t survive the immersion, I wrote. (Though it was kind of a hoot to hear an immortal line delivered as “Stella! … glug, glug, glug … Stella!”) But even sopping wet, Marvel delivered “a performance of remarkable poise and stamina that also locates the tragic, self-defeating conflict in Blanche.”

London, 2002

Glenn Close and Iain Glen

Close brought an “uncommon vigor” and “gymnastic strength” to Blanche, I wrote at the time, while the lithe-bodied Glen appeared merely “to be impersonating coarseness.” When Stanley wrestled Blanche to the bed in the play’s infamous rape scene, “It’s hard to understand why she doesn’t just deck him.”

Washington, D.C., 2004

Patricia Clarkson and Adam Rothenberg

The beguilingly sophisticated Clarkson brought her trademark wit and wryness to Blanche, who emerged here as a calculating strategist and put-down artist instead of a tragic heroine. Rothenberg was an unexpectedly juvenile Stanley. “While you might think that a boyish Stanley would be the perfect match for Ms. Clarkson’s chicken-hawkish Blanche,” I observed, “there is only a weak sexual current between them.”

Broadway, 2005

Natasha Richardson and John C. Reilly

A profound disappointment. After winning a Tony as the life-bruised, sexually voracious Sally Bowles in “Cabaret,” Richardson felt like an exciting choice for Blanche. But for the most part, she seemed aglow with good health and confidence here, and rarely vulnerable. Of Reilly, my review noted, “You sense a real mensch beneath the bluster. Imagine Karl Malden playing Ralph Kramden in ‘The Honeymooners.’”

A pinnacle of my theatergoing life. Liv Ullmann’s production firmly restored Blanche to the center of “Streetcar,” and Blanchett — an actress who always seems to contain multitudes — found every conflicted element of her role’s fractured self, as well as a burning vitality. “What Ms. Blanchett brings to the character is life itself, a primal instinct that keeps her on her feet long after she has been buffeted by blows that would level a heavyweight boxer.” This turned her encounter with Edgerton’s Stanley, a figure of fierce and youthful strength, into a mesmerizing prize fight.

London, 2009

Rachel Weisz and Elliot Cowan

I deeply regret having missed Weisz’s Olivier Award-winning Blanche, who was agreed to be a figure of ravishing, melting contradictions. Writing in The Times, Matt Wolf said, “She is unique among the Blanches I have encountered in communicating afresh the full weight of the delusional Mississippian’s need to put on a performance.” Cowan was evidently just fine as Stanley, barring some mush-mouthed difficulties with his Polish/Southern accent.

The first all-Black “Streetcar” to be staged on Broadway, Blanche emerged here for me as “a lively, self-assured gal, accustomed to manipulating others with her feminine wiles,” while Underwood’s Stanley “comes across as your average overworked husband, understandably testy with that sister-in-law of his always hogging the bathroom.” They exuded “the ease you associate with actors in long-running television series, for whom banter has become second nature.”

Brooklyn, 2016

Gillian Anderson and Ben Foster

Benedict Andrews’s stark, cold-eyed, modernized production presented the war between the in-laws as a brutal Darwinian struggle, which brought out the proto-feminist elements in Williams’s play. Though the approach largely stripped the play of its poetry, for me, it was highly effective. “Ms. Anderson endows Blanche with a self-preserving skepticism that is starting to lose its edge,” I wrote, “and a calculatedly feminine, shrilly Southern persona that feels thoroughly of the moment.” As for Foster’s “effortlessly natural Stanley,” he summoned “the working-class guy who says he’s voting for Donald Trump because he wants America to be strong and virile again.”

As I compiled this list, I became newly aware of how carefully weighted the balance between Blanche and Stanley must be if the play is to engage us fully. For a “Streetcar” to have any dramatic suspense, it requires both erotic chemistry between its leads and a feeling that, until the end, its outcome isn’t predetermined — that its combatants are, for a while at least, evenly matched.

It’s a testament to the mysteries of casting that so many of the stars featured here who didn’t make the grade looked so good on paper. As for Brando himself, in his autobiography he writes that in the Broadway production of “Streetcar,” he felt “Jessica and I were miscast, and between us we threw the play out of balance.” And as for the role with which he will forever be identified, he said, “I was the antithesis of Stanley Kowalski. I was sensitive by nature and he was coarse.”