The presentation forsakes the myth of Modernism that the Modern is identified with — of art as ceaseless progress fomented almost entirely by the innovations of ambitious young (white) men. Instead, it focuses on artists, some famous, some not so famous — Lari Pittman, Ernie Gehr, Joan Jonas — who have just kept on making art, regardless of attention or affirmation, sometimes saving the best for last. The focus here is on art as an older person’s game, a pursuit less of innovation than of authenticity and a deepening personal vision.

The show’s 15 galleries swing energetically between what are essentially small solo exhibitions of works by artists the Modern collects in depth — Jasper Johns, Agnes Martin, Cy Twombly, Gego and David Hammons, who looks great here as both sculptor and painter — and thematic groupings of artists usually represented in the collection by far fewer works, sometimes only one or two. Whatever the category, everything here was made by an artist who was at least 45 — and usually quite a bit older. The oldest is Georgia O’Keeffe, whose seeming abstraction of a white plane receding into blue, titled “From a Day With Juan II,” was made in 1977, when she was 90, and is inspired by the Washington Monument. The painting appears in “The City,” one of the early thematic galleries, among works by Kerry James Marshall, Romare Bearden and Mr. Gehr. A sidebar space is devoted to 11 photographs of New York City street scenes from 1971-81 by the great Helen Levitt (1913-2009), whose gritty poetry hovers ineluctably between color and black and white.

Attention is paid to “late styles,” those unexpected bursts of fresh creativity that some artists summon toward the very ends of their lives, typically in their 70s or 80s. In fact, the show opens with two celebrated examples. In the first gallery stands “Articulated Lair” (1986), a disturbing environment by Louise Bourgeois, who didn’t really begin her mature work until she was past 60. Black on the outside, this folded-screen circle, made of old doors, is mostly blue and white inside. It’s like stepping into a beautiful mind, but dark thoughts intrude in the form of hanging black shapes that conjure sausages, clubs and sides of beef.

The next gallery features Philip Guston’s late style, surrounding us with the brazenly cartoonish, exuberantly tormented figurative works that this apostatic Abstract Expressionist took up in the late 1960s — to the almost universal consternation of the art world — and pursued until his death in 1980. Enormous cherry still lifes and loony faces, macabre chorus lines of legs, hapless-looking Ku Klux Klan figures: These paintings deliver a sardonic commentary on art, art-making, politics and life that never goes out of style.

The exhibition is also an opportunity to show off some recent acquisitions. One of the latest is Ms. Jonas’s “Reanimation,” a majestic yet intimate video-sculpture installation that mixes Arctic landscapes, folk tales, music (by Jason Moran), moving lights and hanging glass, along with views of the artist’s hands, improvising art for the camera. It is near the very end of “The Long Run,” just before the final gallery, where eight of Vija Celmins’s mezzotints of infinite starry nights and ocean waves — also new to the collection — form the serene final fade-out of the show, which has been organized by Paulina Pobocha, an associate curator, and Cara Manes, an assistant curator, in consultation with their department head, Ann Temkin, chief curator of painting and sculpture.

Interestingly, as the aura and familiarity of MoMA-anointed landmarks ebbs and flows, you may find yourself on your own, responding in less filtered ways to what you see. This should occur more frequently, as the museum’s scope becomes increasingly global.

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Other artists in the new-acquisitions category include Thomas and the brilliant assemblage sculptor John Outterbridge. All three of these artists are black, and their belated entry into the collection represents some important course correction on the museum’s part.

The lively, almost noisy exchanges in the “Rampant Abstraction” and “The City” sections are followed by two high-level palate cleansers. First comes a gallery devoted to Martin’s six-canvas work from 1997, resonantly titled “With My Back to the World.” It is worth waiting the few minutes as the paintings’ bands of palest yellow, blue and pink start to bloom. Second, in the next gallery, is Twombly’s “The Four Seasons: Spring, Summer, Autumn and Winter,” from 1993-94, four tall white canvases each of whose marks, colors and scrawled words leave little doubt as to the time of year.

From here, the display reverts to a more hierarchical MoMA mode with the gallery “The Sixties Generation: Color, Form, Pop,” where the curators invite us to consider or reconsider the later efforts of artist stars like Frank Stella, Andy Warhol, Ed Ruscha and James Rosenquist. The day is unequivocally carried by Roy Lichtenstein’s crisp, boldly scaled “Interior With Mobile” (1992), made five years before his death, and Bruce Nauman’s “Dirty Joke” (1987), a two-channel hanging video sculpture. The video features a human jester — a Judy in fabulous green and orange makeup — who waves about a puppet of Punch and fills the gallery with peals of what easily passes as feminist laughter directed at great-man art history.

Things improve with solo presentations of works by Gego, Martin Puryear and Mr. Hammons — his art is footnoted by a small 1938 wall piece made from found materials by Kurt Schwitters, one of the inventors of assemblage. Then there is another group take on the 1960s, but with more thematic power and topicality. Despite its rather flat-footed title, this section, “The Sixties Generation: Materials and Processes,” dwells on the apocalypse. The theme is set by Robert Morris’s mural-size charcoal drawing, from his “Firestorm” series, and its frightening accompanying text, which, especially, makes everything in the gallery click into ominous alignment.

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Black-and-white works by Robert Ryman, Richard Serra and Joseph Beuys suggest bombs, white light and flattened horizons. An On Kawara “date painting” specifies the time: April 24, 1990. The sewn-fabric drawings of Geta Bratescu insinuate melting faces, while Melvin Edwards’s potent little “Lynch Fragment” wall sculptures imply further violence. And in the middle of it all, an untitled hanging sculpture by Lee Bontecou portrays the explosion itself, albeit with insuperable elegance, as if in slow motion