At the moment, Julian Schnabel’s painting seems to be the art that dares not speak its name. Its influence is widely visible but rarely cited. You can see it in the work of artists from Joe Bradley to Oscar Murillo and all sorts of painters who emphasize chance or accident and like to work big, using unconventional materials.


In a sense, Mr. Schnabel was Jeff Koons before Jeff Koons. In the early 1980s he signaled a change in attitude toward art-making — as Mr. Koons would in the late 1980s — and then became a vilified lightning rod. Along with other neo-Expressionists like David Salle, Eric Fischl and Jean-Michel Basquiat, Mr. Schnabel accomplished a liberating take-back for painting. His generation retrieved elements banished during the austere 1970s. They included narrative, language, psychology, the figure (or body) and explicit references to the outside world and past art, which had found refuge with Conceptual, performance, video and photo-based artists. It was as if the painters looked around and thought, if nonpainters can have it all, why not us?


When his white-hot 1980s fame cooled, Mr. Schnabel kept on painting and found other outlets for his talent, directing two extraordinary films, “Before Night Falls” and “The Diving Bell and the Butterfly.” Known for his neo-baroque flourishes and his baronial sense of décor where his living spaces were concerned, he was, for a while, the premier symbol of ’80s excess. But as emerging artists have become more process-oriented and interested in painting on anything but canvas, it is time for some renewed attention to Mr. Schnabel’s art.


Two exhibitions begin this process, one at the Gagosian Gallery on West 24th Street in Chelsea, the other at Karma, an art book publisher with a wonderfully unrehabilitated exhibition space in the East Village. In different ways, both shows stress the spare side of Mr. Schnabel’s supremely instinctive, accepting sensibility.


The Gagosian show comes with a characteristically romantic title that evokes a 19th-century oil study: “View of Dawn in the Tropics: Paintings, 1989-1990.” It presents a dozen large abstract works, some now 25 years old, on tarpaulin, burlap, nylon sailcloth and reversed velvet. All were made outdoors in either Florida or Montauk — so weather and sometimes the ocean contribute — and conventional paintbrushes were largely replaced by sticks, brooms, hands and fingers, and twisted cloths dipped in paint and thrown at the surface.


Two of the smaller untitled paintings in the show — swishes of purple on deep green tarp — are duds or need more work, compared with a larger related effort. That one supplements the purple-on-green-tarp foundation with a rectangle of white muslin and a vertical shape painted gold, with horizontal branches. With mostly scalloped edges, this weird, pronged thing plays the part of a phantasmagoric tree, a gilded frame or a cloud to the rectangle’s window, mirror or boxy moon. The puckering of the tarp seems part of the whole: found ruching.


Mr. Schnabel’s strange combination of bluster and warmth, his intuitive sense of scale and gesture and his love of evoking, mocking and modernizing the past are all evident here. Three paintings — big slurps of white gesso and amber-colored resin on weathered burlap — have the intimacy of immense automatist drawings.


Three other 16-foot-square paintings on red reversed velvet celebrate the ducks of the Retiro Park in Madrid. Their compositions include sewn seams, patches of white or black, occasional words and the grained imprints of the tossed cloth, looking like old engravings (or feathers). The best has a cloudy aspect: the remains of a starter coat of black gesso, rinsed off in the ocean.


“A Little Later,” a lively froth of white and purple, applied with tossed cloths and some smearing, is an unusually delicate gloss on Abstract Expressionism. The large “Ozymandias,” which harbors a shape that might be the desert ruin of the Shelley sonnet with the same title, is the ostensible star of the show, but in this company it tries too hard.


At Karma, “Julian Schnabel: Flag Painting” presents lighter fare that benefits from Mr. Schnabel’s talent for interior décor. Here, white-paneled walls are dotted with 11 new works executed on flags, banners and pennants made of cheap fabric that occasionally use national colors (say, Germany’s red, yellow and black). Mr. Schnabel, working in a manner that is widespread today, has added to them not much — splashes, thick lines or washes of contrasting color — bringing most to pictorial life.


Four wall sculptures depart cheerfully from his dark, hulking bronzes. They consist of waterworn chunks of bright turquoise Styrofoam adorned with a feathered plume or two — lightness reinforces lightness. Three high-backed armchairs in bronze, painted pink, yellow and blue, with red velvet cushions, are possible thrones.


The totality looks fabulous, at once sublime and ridiculous, and, like the efforts of many young painters, brings the medium into three dimensions and closer to the decorative arts.


Karma’s show coincides with its release of “Draw a Family,” a brick of a book that sweeps without benefit of text through Mr. Schnabel’s entire career, from 1973 to the present. That’s 41 years and many paintings that look extremely interesting.


These exhibitions give but glimpses of Mr. Schnabel 25 years ago and today, both ahead of his time and in step with it, skillfully coaxing out the inner paintings in all sorts of ready-made surfaces. It is long past time for some American museum to give him his due.


A version of this article appears in print on April 26, 2014, on Page C2 of the New York edition with the headline: Recapturing the Past, and Then Revising It.