The Museum of Modern Art has never known quite what to do with Willem de Kooning. You can package Jackson Pollock as drips and Barnett Newman as zips, but de Kooning, who painted both opulent abstractions and big, blowsy dames, resists easy branding. So, apart from a show of late work in 1997, the museum has neglected him, until now. With the opening of “De Kooning: A Retrospective” this coming Sunday decades of overdue debt are paid in full. The show, which fills MoMA’s entire sixth floor with some 200 paintings, drawings and sculptures, is exhaustively comprehensive, exhaustingly large and predictably awe inspiring. It not only positions de Kooning far forward in a 20th-century American cavalcade of stars, it turns his career into a kind of Rose Bowl float of creative exuberance and invention. Most usefully the show lets de Kooning be complicated: it presents his art as a bifurcated yet unitary phenomenon. John Elderfield, chief curator emeritus of painting and sculpture at MoMA, unfurls seven decades of work through seven galleries. In each we see abstract and figurative paintings of roughly the same date not just side by side but also interacting, intertwining, merging identities; abstraction breathes, smiles and bleeds; figures shimmer and shudder apart into color and line. In its shape the show adheres to a classic cradle-to-grave survey model, beginning with a still life that de Kooning painted at the age of 12 in his Dutch hometown, Rotterdam. By his early teenage years he was already working in a commercial design firm, where he learned sign-lettering and paste-up techniques like tracing, copying and layering. All of this came in handy while looking for work when he first arrived, after stowing away on a freighter, in the United States in 1926. More important in the long run, his design training, with its emphasis on creating an organic-looking whole from many pieces, ended up as the formal bedrock of his art. He was lucky in being, by temperament, chronically hungry and omnivorous. In the first two sections of the show, which take us in giant steps up to 1949, we see him devouring his way through visual history past and present, gobbling up images from Ingres, Rubens, Soutine and Picasso; from contemporaries like Arshile Gorky; and from movie ads, Sunday comics and the graphics in New York police gazettes. While some artists and thinkers of the day were promoting an art of utopian purity, one that required shutting a door between art and life, de Kooning’s appetite took him in the opposite, though really no less utopian, direction. He wanted to open everything up, to bring — to squeeze — everything into art: high, low; old, new; savagery, grace. And so he did, in a laborious, pieced-together, piled-up, revision-intensive way. Far from being the sort of impulsive, gut-spilling artist implied by the term “action painting,” he was a deliberator. Every painting was a controlled experiment. Typically he would start with a drawing, add paint, draw on top of the paint, scrape the surface down, draw more images traced and transferred from elsewhere, add paint to them, and on and on. Given this process, it seems astonishing that he was so prolific, until you remember that he was virtually never not working: trying this, tweaking that, scrapping failures, starting afresh. Whenever the enormousness of the MoMA show gets you down, stop in front of one picture, almost any one, and linger. The basic, energy-generating dynamic of de Kooning’s art operates in microcosm in nearly every single thing he did after the mid-1940s. Experiencing the physical mechanics of his art close up, in action, is the real thrill of the show. To engage with it is to meet a person rather than just visit a monument. The late 1940s was when de Kooning first caught fire, when abstraction and figures first merged. That’s the story of “Pink Angels” from around 1945, the final painting in his first series devoted to images of women. From painting to painting, the single seated figure in the series grows less naturalistic, begins to lose its contours, to dissolve into its surroundings. By “Pink Angels” the figures have lost their clothes, lost their faces, and become monstrously voluptuous, approximately human forms made from chunks of cut-up flesh. It’s as if we’re seeing the cleanup phase of a sloppy autopsy, but one that took place inside a chamber of gold. How such a scene can be beautiful is hard to say, but it is. De Kooning once famously observed that “flesh was the reason why oil paint was invented.” It’s important to remember that he wasn’t thinking only of the milk-white flawless flesh of Titian courtesans but also flesh that bruised, bled, rotted away. The vanitas awareness of the 17th-century Dutch still-life painters was strong in him, the bass note to his force-of-life vigor. In “Pink Angels” his nods to Picasso, Matisse and Miró are easy to spot, but one detail, the image of a fish head with the gaping mouth that forms the angel’s foot, is a puzzler. It’s lifted from a 16th-century print of “The Last Judgment” by Pieter Bruegel the Elder. In 1946 de Kooning painted a picture called “Judgment Day.” From a distance it seems vaguely abstract. (Again, much of his work looks vague from afar, particularly in MoMA’s galleries, which are way overscaled for this art.) But up close you see that it’s packed with four crablike figures: the angels of the Apocalypse crouched in a huddle. Significantly, the work that finally put him on the art-world map has no figures, or none in plain sight. His first New York solo in 1948, when was 43, was made up of all-but-imageless paintings. Some were done primarily in black and white, with white paint twisting in thin lines, like cracks spreading in smashed glass sheets, over the dark ground. Within the art world the show was a sensation. De Kooning was declared, by an approving, territory-marking Clement Greenberg, “an outright ‘abstract’ painter.” The skeins of white paint were read as a kind of expressive calligraphy. The reductive palette, which many other artists would adopt, was taken as a sign of existential seriousness. De Kooning suddenly found himself centrally placed within a critical cordon sanitaire set up by Greenberg and others for the development of a new, advanced American modernism. De Kooning could easily have stayed within those bounds, nailing down a signature look and turning out reliable product for reliable reward. But he didn’t do that. He made more black-and-white pictures but simultaneously painted images of women, which no one seemed to notice. In 1953, when he exhibited his third “Woman” series, the paintings were so outrageous that the art world had to pay attention, and did. These pictures of busty Gorgons with slashed-out bodies, flyaway fingers and equine grins caused fits. Instantly accusations of misogyny started flying, though de Kooning’s main sin was his perceived defection from the vanguard program. To true believers the “Woman” paintings were profoundly retrogressive. Looking at them now we can pick up conceptual links, however coincidental, to work by that most radical of outsider-insider artists, Marcel Duchamp, whose confoundingly erotic, morbid and witty “Étant Donnés” was already secretly in progress. And through the wide-angle view afforded by a retrospective we can see thoroughly, and logically, how abstraction and figuration interlocked in de Kooning’s art of this time. We can also imagine how difficult it must have been for him psychologically to sustain both modes in the face of an establishment that wanted only one and vehemently rejected the other. Over all de Kooning’s output through the 1950s gives a sense of being made under exceptional pressure. The energy is fixed at crescendo level. The surfaces in paintings like “Gotham News” (1955) are ugly-thick and distressed. The colors are chaotic, with streaks of red jabbing out like police-car lights. Everything looks frenzied and noisy, as if done to the sound of alarms. Then there’s this absolutely amazing change of tempo and atmosphere, like the moment in a Mahler symphony when grinding marches stop, and you’re in a pastoral realm of cowbells and celestas. In the late 1950s de Kooning started spending time outside New York City. He moved permanently to the Springs on Long Island in 1963. “Rosy-Fingered Dawn at Louse Point,” with its references to Homer and to a spit of land and sea near his new studio, dates from that year. With its jonquil yellows, bluebird blues and Tiepolo pinks, it has a lifted-up joyousness unseen in his art before. The calm didn’t last. More women arrived, undulating and splitting open like wounds. So did de Kooning’s first sculptures: blobby, woozy little bronze figures that turn into blobby bigger figures. The impression made in this section of the show is of prolix distraction, with drawings of crucifixions, images of Picassoid satyrs, and oleaginous paintings that suggest food-processor versions of earlier things. The 1980s brought another clearing out. Suddenly there are just three colors, Mondrian’s primaries — red, yellow and blue — drawn out in thin banners over pure white fields. By this point de Kooning was showing sign of Alzheimer’s disease, which was far advanced by 1987, the year of the show’s last painting. When this late work appeared at MoMA in 1997, the year de Kooning died, some dismissed it as a mere byproduct of pathology. I admire a lot of de Kooning; I love these last pictures. If Mr. Elderfield’s exhibition had done nothing more than provide a context for them, it would have done a lot. Of course it does much more. In its scale, crème-de-la-crème editing and processional sweep it’s MoMA in excelsis, and for many people it will probably represent this institution’s history writing at its best. Yet for a while now the museum has been immersed in another history writing project, and an even more essential one, in its continuing and undersung efforts to historicize Conceptualism, the single most influential art movement of the last third of the 20th century. Conceptual Art, in its classic 1960s form, might appear, at first glance, to be the very opposite of de Kooning’s art, though they have much in common. Both are equally obsessed with the material world, whether in trying to erase or embrace it. Both privilege ideas above ego. (De Kooning said many times that his art incorporated but was not about personal expression.) And both are fundamentally expansive in spirit. Conceptualism keeps open a door through which all kinds of fresh creative impulses can flow. The art of de Kooning, so generous and undoctrinaire, does the same.