San Francisco acupuncturist refers to any procedure requiring many needles as “The Full Frida Kahlo.” He assumes his patients are familiar with Kahlo’s self-portrait, Diego on My Mind, in which wiry tendrils radiate from her head, or The Broken Column, in which flathead nails stick out all over her head and body. A woman I know once went to a costume party dressed as Frida Kahlo, no explanations needed. Imagine going dressed as Helen Frankenthaler or Grace Hartigan or even Georgia O’Keefe. That would keep them guessing. For Kahlo self-portraiture was icon-making. No artist of the modern period except Van Gogh — not even egomaniacs like Dalí, Picasso, and Gorky — made self-portraits so immediately identifiable to so many people. They are not just representations of a self, they are blazons of a self in pain. An automobile accident when she was 18, and the many surgeries that ensued, caused her lifelong agony and prevented her from bearing children. In the paintings, it and other kinds of emotional pain come tightly wrapped in a severe, judgmental visage.

During the big Cézanne retrospective in Philadelphia a few years back, city buses were painted over with the master’s still lifes. Cézanne made many self-portraits, but the promoters knew that a still life was more recognizable than his face. All over San Diego, banners bearing Frida Kahlo’s image announce a good, selective show of modern and contemporary Mexican art from the Jacques and Natasha Gelman collection. Don’t be misled. It’s not a Kahlo show, though she has more pictures in it than anyone. Thirty-six artists are represented, from the classic politico-muralists Diego Rivera, José Clemente Orozco, and David Alfaro Siqueiros, who played major roles in the development of post-revolution Mexican art, to young (often equally political) contemporaries like Paula Santiago, Francisco Toledo, and Francis Alys.

I’ll get this out of the way right now: Kahlo’s work either gets to you or it doesn’t, and to me it doesn’t. She represented her body as a construction and demolition site. I like her seditious, mocking wit and sardonic solemnity, and her imagery can be unsettling, but as painting, the work is stiff (even when she’s depicting tropical abundance in a still life containing watermelons, bananas, and mangoes) and the over-controlled icon-making has a faint stink of sanctimony. By operatically displaying the body suffering symbolic and actual agonies of all kinds, she makes suffering seem perversely glamorous. For all their apparent daring, most of her pictures are buttoned down. Even when there are surprising details, like the needle-beaked bird of paradise flower in Self-Portrait with Monkeys and the papier mâché baby doll in Self-Portrait with Bed, it’s canned surprise, locked into a symbolic structure. Once we get it, we get it.

The works constellated around Kahlo’s pictures make a vest-pocket history of modern Mexican art. Diego Rivera, her husband on and off for 25 contentious years, has pride of place with nine pictures. A trip to Italy in 1920–1921 to study Renaissance frescoes prepared Rivera for large mural projects he later executed in Mexico and the United States. That experience carried over into his easel painting. The drapery of a woman’s shawl in The Healer, a conventional genre piece, looks like a detail from a Giotto fresco. Rivera, a superb colorist, knew how to stuff pictorial space to the bursting point. In Calla Lily Vendor, where only the vendor’s hat is visible mushrooming behind the enormous blooms, the space teems with tropical abundance. There’s never a stingy or pinched moment in Rivera’s work. Nature for him is a place of menacing gigantism. The sunflowers in one picture look like earth gods about to devour or reclaim the children playing among them.

Orozco had the aggressive, deft hand of a good draughtsman. His figure studies are graceful and airy, yet they have a meaty feeling for rough embodiment. Like other great graphic artists, Orozco, who lived briefly in Los Angeles designing movie posters, achieved racy completeness with an economy of means. A small 1932 Self-Portrait in watercolor and gouache is so righteously drawn that I felt its gaze following me around the room. It’s also psychologically accurate; Orozco was famously surly and difficult. He lived in New York from 1927 to 1935, and the whipped up anti-bourgeois dynamics in his larger pictures suggest the broad effects and political edge of American Ash Can painters of the 1920s like John Sloan. Orozco was the articulate savage. He liked to say that “one has to paint with shit.”

I wish there were more pictures in the exhibition by Siqueiros. His operatic Woman with Rebozo is the most exciting painting on view. He’s the one who really pushes paint around. The surfaces of the Rebozo picture and Head of a Woman have a churned-up velocity; you can see the pigment being swept into forms with the kind of excited, heavy impasto — slabs of paint laid in with big brushes — that makes you want to run your hand across the surface. And yet it’s Siquieros who believed most strongly that mural painting was the supreme form of expression.

In 1923, the three put their names to a manifesto that said, “We reject as aristocratic the painting known as ‘easel work,’ along with the entire ultra-intellectual cadre; and we exalt expressions of monumental art for being useful to the public.” All three, of course, never hesitated to do easel painting. Their fondness for the monumental and rejection of aristocracies have bled down into art being produced now. Monumentalism meets bad-boy-ism in Miguel Calderón’s big color photographs, each a pleasurably nasty one-liner. One shows an Afro-ed, casting-call bandito type holding a gun to the head of a zebra! Two others, from the series “Greetings from My Hairy Nuts,” satirize postcard prettifications of Mexico by blending into famous tourist locales close-ups of Mr. Calderón’s anatomical locale.

The two most exciting young artists included here are Francisco Toledo (b. 1959) and Elena Climent (b. 1955). Climent makes lush, painterly still lifes. Her Blue Pail looks gigantic, though it’s only 11˝ x 9˝, because of the way the pail expands hugely up through the frame. Toledo is a draughtsman with good hands; he’s more interested in creating an almost monstrous prolixity of line than in pushing paint around. His 1987 Self-Portrait with Hat is built of stacked, choppy Vs, and his 1975 Rabbit of the Scorpions, in which dozens of ghostly scorpions wheel in a sand storm (there’s sand in the picture) around a skinny, helpless rabbit, is a classic Mexican image of nature as a field of riot and death. Working different sides of the street, both artists have felt their way through the residual pressures of modernism to find a fresh, contemporary idiom. Paula Santiago’s art is more idea-driven, less pressured by formal concerns. She crafts bibs, baby clothes, breastplates, vests, and other articles of clothing out of rice paper, blood, hair, and wax. Like many other artists experimenting with dress art, she’s investigating “gender issues” and their historical origins. Her four pieces in the show quiver with “issues.” But they do what good art does. They upset expectations. I thought they’d be inert, over-conceptualized, academic, but in fact they are disturbingly beautiful and have haunted me more than anything in the show.