“Arthur Miller: Writer,” a new HBO documentary about the playwright’s life and work, was produced and directed by Miller’s daughter Rebecca, who collected footage for it for more than twenty years. Often, she was able to shoot from intimate or rarified vantages: her father carving a freshly roasted chicken, reading the newspaper, picking up a pair of bluejeans from the floor and putting them back on. “I felt I was the only filmmaker that he would let close enough to really see what he was like,” she explains, in an early voice-over. In conversation, Miller exhibits deep intelligence and an almost preternatural grace—he appreciates both the inanity and the magnificence of living. While reflecting on his experiences, he will often say something casual but unbearably profound, like “People are far more difficult to change than I had allowed myself to believe.” (Oof.)

Rebecca, who is fifty-five, has also worked as a filmmaker, novelist, and painter, and is married to the actor Daniel Day-Lewis. She is a child of Miller’s third marriage, to the Austrian photographer Inge Morath. Her father’s romantic relationships occupy a good chunk of her movie. In 1940, Miller married Mary Slattery; in 1951, he met Marilyn Monroe. “It wasn’t enough for me, suddenly,” Miller admits of his first marriage. He and Monroe began exchanging letters, which were filled with yearning. For the next five years, Miller struggled to metabolize his guilt and anger: “I no longer knew what I wanted, certainly not the end of my marriage, but the thought of putting Marilyn out of my life was unbearable,” he writes in “Timebends,” his autobiography, from 1987. He went to work each day past a life-size cutout of Monroe—the famous shot from “The Seven Year Itch,” in which she’s laughing, her white skirt billowing up around her.

Ultimately, Miller couldn’t live without her. His correspondence with Monroe grew breathless, desperate: “It is just that I believe that I should really die if I ever lost you,” he wrote. “It is as if we were born the same morning, when no other life existed on this earth.” They were married in 1956, but divorced by 1961. She overdosed on sleeping pills in 1962. When Miller speaks of her, he sounds both enamored and defeated.

Miller was radicalized in the nineteen-fifties, and, like many of his colleagues, he was investigated by the House Un-American Activities Committee. He was eventually found guilty of contempt of Congress, for refusing to provide the names of people he had seen at meetings of the Communist Party. “A kind of popular fascism was developing in the United States,” Miller explains. The debacle fed the work (you get the sense, with Miller, that everything eventually fed the work), and, in 1953, he wrote “The Crucible,” a play ostensibly about the Salem witch trials. It’s also a trenchant allegory of McCarthyism and a raw display of the kind of swelling, blinding panic that can seize hold when people feel truly helpless.

Miller married Inge Morath, in 1962, and they were together for the next forty years. Miller was, perhaps, less pie-eyed about love by then. “I miss you. I am discouraged with myself, my rootlessness. And ashamed too,” he wrote to her. “I can’t talk to anyone but you about so many things. I feel haunted sometimes by the question of whether anything, any feeling, is eternal.” Miller was trying to make sense of it all on the page. The film includes poignant and insightful interviews with the playwright Tony Kushner—perhaps Miller’s only real peer—and the writer and director Mike Nichols. Both speak admiringly of Miller’s ability to sublimate his own pain into prose.

The film also bravely addresses Daniel Miller, Miller’s son with Morath, who was born with Down’s syndrome in 1966, and institutionalized shortly thereafter. “I found myself not doubting the doctor’s conclusions, but feeling a welling up of love for him,” Miller wrote in his journal, in 1968. “I dared not touch him, lest I end by taking him home, and I wept.” Though Miller did not mention Daniel in his autobiography, he did agree to speak to Rebecca about him—yet the conversation never happened. “I had the opportunity to finish this film in the nineteen-nineties, but I didn’t know how to finish the film without talking about my brother, and I didn’t know how to do that,” Rebecca explains in a voice-over. “I told my father this, and he offered to do an interview about it. I put it off. I put it off for a long time. I had children, and I started making other films, and he died.”

The film conspicuously doesn’t attend to Miller’s last girlfriend, the painter Agnes Barley, who was thirty-four years old at time of his death. Barley met Miller a few months after Morath died, in 2002, and moved into his Roxbury, Connecticut, home the same year. In a gossip column, the Daily News suggested that Rebecca and Day-Lewis were disapproving of the relationship and its more than fifty-year age difference, and that they asked Barley to leave Miller’s estate following his death, in 2005. The precise dynamic of Miller and Barley’s relationship remains unclear—some sources report they were engaged.

I met Miller once, briefly. He was eighty-seven, and had been invited to speak to a graduate seminar I was taking at Columbia University, on memory as a kind of literary engine. (It was taught by the wonderful poet Honor Moore, Miller’s friend and neighbor in Roxbury.) We were seated around a formidable wooden table—the same one where we gathered to dissect our own stories and attempted to sniff out what we were doing wrong, and what (if anything) we were doing right. I recall feeling awestruck when Miller walked into the room. He had been adjacent or pivotal to so many extraordinary moments, and “Death of a Salesman” is as formative and essential an American text as I can think of. Though Miller looked his age by then, he spoke about the strange and difficult work of writing with a sharpness and acuity that I found staggering. He seemed to have figured something out.

In 2015, the centennial of Miller’s birth, the Belgian director Ivo van Hove staged a minimalist production of “A View from the Bridge” at the Lyceum Theatre, on Broadway. A friend and I got tickets for opening night. The play is set in Red Hook, Brooklyn. “This is the slum that faces the bay on the seaward side of Brooklyn Bridge,” Miller writes. “This is the gullet of New York swallowing the tonnage of the world.” If you have ever spent any time there, considering Buttermilk Channel from the cusp of Valentino Pier, you understand that Red Hook—with its vast and desolate waterfront, overlooking the Statue of Liberty—is a place that accommodates a certain amount of longing.

“A View from the Bridge” is a tragedy in the Greek sense. Eddie Carbone, a married longshoreman, falls in love with his orphaned niece, Catherine. His situation—like all furious, intractable, predatory loves—is doomed from the outset and grows increasingly untenable, as Eddie, who is clearly terrified, makes more strange and awful decisions. “His value is created largely by his fidelity to the code of his culture,” Miller wrote in 1960, in an introduction to the play. “Invisibly, and without having to speak of it, he was getting ready to invoke upon himself the wrath of his tribe.”

Miller is interested in implacable appetites—you can sense his own, in his letters to Monroe—and in the ways in which we are punished for them. The punishment part is important: “In a word, I was tired of mere sympathy in the theater,” Miller wrote in his introduction to “A View from the Bridge.” It would require extraordinary hubris to call Eddie “bad,” in the judgment-day sense, but he nonetheless mismanages his lust and envy in unforgivable ways. Whenever I caught myself feeling sympathetic toward him, I felt enormous shame—Catherine is just seventeen, and thinks of Eddie as a paternal figure, a trust he systematically sullies and exploits. Nonetheless, his predicament reminds me of a line in “Death of a Salesman”: “He’s not the finest character that ever lived,” Linda Loman says of her husband, Willy. “But he’s a human being, and a terrible thing is happening to him. So attention must be paid.”