Her son Charlie Whitehead said Caldwell died peacefully Sunday at her home in Pound Ridge, New York. Whitehead said her death was due to complications from Parkinson's disease.
The Australian-born actress played in regional theaters around the English-speaking world before becoming the toast of Broadway in 1968, and winning her second Tony, for "The Prime of Miss Jean Brodie."
Among her other characters were Cleopatra, Saint Joan, Mother Courage and authors Colette and Lillian Hellman. As she matured, she accepted only roles that offer a particular challenge. If she thought, "Oh, I can do that," she didn't want to do them, she said in 1986.
Three of her four Tonys came in collaborations with her husband, Robert Whitehead, who was one of Broadway's most prolific producers of serious drama.
She cited his influence in her decision to do "Medea," the ancient Greek drama of a woman who is betrayed by her lover and kills their children in revenge. It won her a third Tony in 1982.
"Medea wasn't a character I believed in until my Robert started to talk to me about her in human terms," she told The New York Times a few days after the Tony ceremony. "I suddenly understood how a creative force of nature can become destructive if it is mucked up, polluted, depurified — like the atom."
Times critic Frank Rich cited the flashes of sensuality — which she said derived from the study of Greek painting and sculpture — and wit that she brought to the character.
"When, at last, the crime is at hand, the actress fully dramatizes the struggle between her hunger for revenge and her love of her sons," Rich wrote. "Like the gods, we can understand, if not pardon, the primal impulse that drives her to the ultimate act of annihilation."
Terrence McNally's "Master Class," which debuted on Broadway in 1995, was another joint effort with Whitehead. It won Caldwell her fourth Tony and brought Whitehead, as producer, the Tony for best play.
She played Callas as the opera superstar critiques, cajoles and inspires a trio of budding singers taking part in the uniquely intense musical education session called a master class.
"A performance is a struggle. You have to win," she says as Callas.
Then-Associated Press drama critic Michael Kuchwara called Caldwell "incandescent" and said she gave "the performance of her career."
Already well-known to those who followed regional theater, she had made her Broadway debut in "The Devils" in late 1965, temporarily replacing for Anne Bancroft, who injured her back.
Caldwell was quickly announced for a role as a society columnist in "Slapstick Tragedy," Tennessee Williams' pair of one-act plays. The production lasted less than a week on Broadway in February 1966 — but it brought Caldwell her first Tony, for best featured actress.
Broadway stardom arrived two years later for "The Prime of Miss Jean Brodie." The story of an eccentric Scottish schoolteacher with pro-fascist tendencies originated as a novel by Muriel Spark. The role had already been successful for Vanessa Redgrave in London and would eventually win an Oscar for Maggie Smith.
The Washington Post, noting others had played the role, said that "so masterfully exact is Miss Caldwell that watching her you will probably feel that hers is the only way (to play it). ... Almost at the instant we first see Miss Brodie, the actress has found a perfect mannerism."
The New York Times said Caldwell "flounces onto the stage like a sparrow with illusions of grandeur."
She and producer Whitehead married later that year. She told writer Rex Reed that far from pushing her into the Brodie role, Whitehead "wasn't keen on me for the part" until the playwright, Jay Presson Allen, campaigned for her.
Caldwell added Broadway directing to her resume starting in 1977 with a comedy, "An Almost Perfect Person," starring Colleen Dewhurst. In 1991, she directed Jason Robards and Judith Ivey in "Park Your Car in Harvard Yard." She was last on Broadway in 2003 as the Mystery Guest Star in "The Play What I Wrote." She also lent her voice to the "Lilo & Stitch" cartoons and appeared in the 2011 film "Extremely Loud & Incredibly Close."
She spent much of her early career on the road.
After touring in a wide variety of plays in Australia, she came to England and got to tackle a succession of Shakespearean roles.
"I was always afraid of growing comfortable, so I would jump from job to job, whatever I was offered," she told The Associated Press in 1986. "I would go from Stratford-on-Avon to a small repertory company and back to London."
She traveled to Canada for parts at the Stratford Shakespeare Festival. In the United States, she did regional theater work at the Guthrie Theater in Minneapolis and the Goodman Theater in Chicago.
At that time, she said she didn't turn down any job.
"It was a heck of a long apprenticeship, but I would recommend it to any actress," she told The New York Times in 1968.
Caldwell was born in 1933 in Melbourne, Australia, to a family struggling to make it through the Depression. In her memoir, "I Will Be Cleopatra," she wrote that she knew at an early age that her job would be "keeping audiences awake and in their seats."
"I knew this because it was the only thing I could do," she wrote. Despite the family's tight budget, the Caldwells were regular theater-goers, she wrote, and "I saw every singer, dancer, actor, or vaudevillian who came to Melbourne."
She made her stage debut at age 9 in a Melbourne production of "Peter Pan."
Her husband died in 2002 at age 86, shortly after he had received a special Tony Award for his nearly 60-year career. Among his other honors were a best play Tony for "A Man for All Seasons" in 1962 and a best revival Tony for "Death of a Salesman" in 1984.
She and Whitehead had two sons, Sam and Charlie. In addition to her two sons, she is survived by two grandchildren.
"I always knew I would be an actor. I am an actor," she told the AP in 1986. "But being a wife and a mother still seems to me to be some kind of extraordinary stuff."