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How do you get Leonardo DiCaprio talking? Put him in a room with Paul Thomas Anderson. During hours of conversation, two era-defining men-on the record together for the first time-went deep. They cracked some jokes, too.

- Photographs by Paul Thomas Anderson Styling by Warren Alfie Baker

Shirt and trousers by Loro Piana; Oyster Perpetual 41 watch by Rolex; sunglasses by Brunello Cucinelli.

A LEONARDO DICAPRIO performance is always an intense experience: Howard Hughes losing his mind, Jordan Belfort debasing himself, Hugh Glass surviving against all odds. We are watching one of Hollywood's greatest of all time at work. His latest film, One Battle After Another, is no exception. DiCaprio plays Bob Ferguson, a washed-up revolutionary and dad to a teenage daughter, Willa, played by Chase Infiniti in her first film role. Opposite him are Teyana Taylor as the absent mom, Benicio Del Toro as the ally, and Sean Penn as the villain. One Battle After Another is a big movie—an action film with car chases, a spycraft yarn with a clandestine agent who's drunk and stoned, and a political thriller with reverberations for our interesting times. But at its core, the movie is a story about a father and daughter and what it means to show up for the people you love. It's also very funny.

The writer and director is Paul Thomas Anderson, whose films—like Boogie Nights, Magnolia, and There Will Be Blood—are operatic renderings of human frailty. The movies are visceral and often haunting. They can also be hilarious, and they're always wildly entertaining.

One Battle After Another is his first film with DiCaprio. Both men rarely give interviews, and their life and work are the subject of bottomless curiosity and speculation. This summer, they had two conversations: one in Leo's kitchen, another over the phone. They recorded their talks and gave the transcripts to Esquire, which we edited and condensed. (Anderson also photographed DiCaprio for us in Los Angeles.) We gave them some prompts, some of which they indulged, others not so much. But the result is a rare glimpse into the minds of two of Hollywood's most daring and original men.

PAUL THOMAS ANDERSON: Any regrets?