We amateurs commonly speak of “taking a picture.” Those who practice photography more seriously used to grumble, “I don’t take pictures— I make them.” Point taken, but circa 1980, artists like Richard Prince and Sherrie Levine started talking about, and doing, what they called “appropriation.” Influenced by the conceptual art of the preceding decade, and haunted by the sense that pictures make us more than we do them, they tried out a second-order photography, making pictures by, literally, taking them from consciously artistic sources (Levine’s works “after” Walker Evans or Dorothea Lange) or purely commercial ones (Prince’s Marlboro Men). Theirs were images of images, photographs in quotation marks. Meanwhile, as if to prove the priority of images over real life, Cindy Sherman was populating her “Untitled Film Stills” with images of herself as the stereotypical heroines of imaginary B-movies. For all three artists, the idea was not to use photography to picture the world but rather to picture photography: to envision and perhaps undermine the existence and operations of a medium that, after more than a century, was now taken for granted.

Photographic appropriation—rephotography—is still very much with us… and there’s so much more to rephotograph! Found digital images don’t even need to be rephotographed to be reused; just click “Save As…” But how is an artist to navigate this flux of imagery? In their very titles, two current exhibitions at New York City museums emphasize two possible approaches. At the Museum of Modern Art, “Ocean of Images: New Photography 2015” (on view through March 20) seems to put the focus on how images have become a kind of total environment in which we find ourselves immersed. The nearly concurrent exhibition at the Solomon R. Guggenheim Museum, “Photo-Poetics: An Anthology” (on view through March 23)—its title calling attention to the idea of poiesis, Greek for “making”—­has a dual emphasis: that the artist’s task has to do with making something of what one gathers from the ocean of images, and that whatever is so made will have the essentially discursive, perhaps even erudite character we associate with poetry and poetics.

The MoMA show is the latest in its “New Photography” exhibition series, which was inaugurated by John Szarkowski in 1985 and has been offered nearly every year since. With works by 19 artists (including one collective) from 14 countries, the latest show seems like the most extensive. That “Ocean of Images” wasn’t meant to be the kind of exhibition that would have pleased Szarkowski—a curator whose name is indelibly associated with the emergence of such figures as Diane Arbus, Lee Friedlander, and William Eggleston—is obvious from the get-go. The first work on view, also highlighted in the show’s publicity, is by the New York–based group Dis: a video installation featuring the Austrian pop singer and drag queen Conchita Wurst, the winner of the 2014 Eurovision Song Contest. Szarkowski would not have been averse to images blurring the gender line—he showed Arbus’s photos of transvestites—or even to MoMA’s stepping off the pedestal of high culture to endorse the low-brow celebrity of the Eurovision Song Contest; with his embrace of the “snapshot aesthetic,” Szarkowski had already crossed the high/low divide. But to give pride of place in a new photography show to a video by artists who don’t think of themselves as photographers, but as makers of “cultural interventions…manifest across a range of media and platforms”—this would have given him pause.

Even more surprising to him might have been the inclusion of Lele Saveri’s installation The Newsstand (2013–14). It’s a full-scale, three-dimensional simulacrum of a subway newsstand, only with artists’ zines substituted for the standard fare of daily papers, weekly gossip rags, and monthly fashion bibles. There’s also Katharina Gaenssler’s Bauhaus Staircase (2015), a wall papered with photocopies of images of the building that housed the famous German art school at its second location, in Dessau. Indre Serpytyte’s works in the show include small wooden sculptures of “houses, barns, and official buildings that served as the stage for atrocities committed by the NKVD (People’s Commissariat for Internal Affairs), the [Soviet] military police during World War II; the MGB (Ministry of State Security), the Soviet intelligence agency from 1946 to 1953; the KGB (Committee for State Security), active from 1954; and the Soviet MVD (Ministry of the Interior).” Serpytyte commissioned Lithuanian woodcarvers to sculpt the structures in her photographs. But in the exhibition, the black-and-white prints of these buildings are not the ones on which the carvings are based, but rather images at a third remove from the originals: photographs of the carvings of photographs of the buildings.

The inclusion of such works, not to mention other video pieces by Dis, Zbynek Baladran, and Mishka Henner, suggests that for the curators of “Ocean of Images”—Quentin Bajac, Lucy Gallun, and Roxana Marcoci, with the assistance of Kristen Gaylord—­photography is no longer a particular medium or practice, but more like a set of questions about the perplexed relation between images (whatever they are) and reality (whatever that is). An image is always supposed to be of something; it is merely a secondary substitute for something else, a sort of reminder. But images also constitute reality; they can change minds. They don’t just represent things; they specify, they select, one might even say they elect certain things as being worth representation. As Szarkowski once put it: “One might compare the art of photography to the act of pointing…. It must be true that some of us point to more interesting facts, events, circumstances, and configurations than others.”

The ever-greater overproduction and hypercirculation of images that began with the invention of photography in the 19th century has increased exponentially thanks to the digital revolution. The result has been a kind of leveling, as it has become harder and harder for images to show us that particular “facts, events, circumstances, and configurations” are more interesting than others; it’s much like imagining that a single drop in the ocean is more significant than the rest. As Bajac told an interviewer for Aperture magazine after arriving as MoMA’s new chief photography curator in 2012: “The main concern for curators in the 1960s, ’70s, and even early ’80s was to provide access to photographic images. Now we have too much access to too many images…. I think it is important now for us curators to be able to educate the public and to direct them in this ocean of images.”

In this instance, Bajac and his colleagues have done a better job of pointing to the ocean than of charting any clear course through it. Maybe the best option, for now, might be continuing to act as if one could still collect significant drops of water from it. This seems to be the approach suggested by one of my favorite artists in “Ocean of Images,” Natalie Czech. Her works take the form of photographs—chromogenic color prints, if that matters—yet they elide the photographic tradition that Szarkowski upheld just as effectively as any of the show’s sculptures, videos, or installations. Czech’s preferred subject matter is poetry, mainly but not exclusively what used to be called “the new American poetry,” after the landmark anthology Donald Allen published under that title in 1960: the whole raft of anti-academic tendencies (Beats, Black Mountain, New York School) that emerged after World War II.

We’re always being told to find poetry in the everyday, and sometimes it really happens, but no one’s ever found it in quite the way Czech does. Take her triptych A Poem by Repetition of Allen Ginsberg (2013), which shows three views of the same page of an art-magazine article about Robert Longo, featuring an image from his “Men in the Cities” drawing series of the early ’80s. By highlighting isolated words and phrases in the article, Czech has managed to “discover,” as if through divination or by a dubious process of implantation, some lines of Ginsberg’s in a text to which they are completely irrelevant. Perhaps less of a challenge was finding, for A Poem by Repetition of Aram Saroyan (2013), one of the minimalist poet’s works—“ney / mo / money”—in three copies of the sleeve of Pink Floyd’s 1973 hit single “Money,” with a few of the letters blacked out. Does the ability to find it anywhere make poetry more or less precious? Czech somehow manages to adulate poetry and question it all at once.

That ambivalence marks much of “Photo-Poetics” as well. Although the exhibition, organized by Jennifer Blessing with Susan Thompson, also includes several videos (by Erin Shirreff and Moyra Davey) as well as a couple of slide-projection pieces (by Lisa Oppenheim and Kathrin Sonntag), its emphasis falls more firmly on the individual photographic print. Perhaps that’s why the mood at the Guggenheim is far more retrospective, melancholic, and too often academic than the messier, more exasperating, but livelier show in midtown. For all that, I prefer the Guggenheim’s take on the current state of photography: Reflectiveness is its virtue.

Appropriately enough for a show that encourages the viewer to devote time to looking at each work, “Photo-Poetics” is less extensive than “Ocean of Images,” featuring just 10 artists, all based in either the United States or Germany. Nine of the artists are women. I was particularly taken with the works from Leslie Hewitt’s 2006–09 series Riffs on Real Time. Each uses the same basic structure: a snapshot, a vintage personal photo (whose, we don’t know), has been placed on top of a book or magazine, open or closed, which has been placed on a floor (carpeted, bare wood, whatever). The whole setup has then been photographed straight on from above, with the sort of forensic objectivity that is common to many of the works in the show.

In contrast to Prince, Levine, and many of their successors, Hewitt’s second-order photography emphasizes that printed images are material objects in a given space, things as well as signs. She’s also underlining, I think, the dichotomy between the cool professionalism with which she has made her work and the clumsy, amateurish ways of the found snapshots—­no thumbs in them, but still, every other mistake in the book. (The book would be Kodak’s manual How to Make Good Pictures, a copy of which she incorporated into her installation for the 2008 Whitney Biennial). But Hewitt presents these slapdash snaps without condescension. With their elaborate internal framing, her works seem to insist that the emotional core of an artwork lies precisely in its raw, nearly uncontrolled responsiveness to daily life, the inadvertent slippage from pictorial conventions that such vernacular images can sometimes embody—while at the same time keeping in mind that this imagery only becomes art when it is deliberated and given distance by aesthetic self-consciousness.

Hewitt’s concern with photographs as subject matter—not only with photographic imagery, but with these printed images as objects in the world with their own histories—­is shared by several of the artists in “Photo-Poetics.” Erica Baum’s photographs include several in which she’s captured stills from old movies—titles like Jaws and Shampoo (both 2008) presumably reveal the original source—but we see them only obliquely, because they’ve been made by riffling through a book and photographing the partly visible pages. The black-and-white film still appears as merely the most legible fragment amid yellowed pages with decoratively stained edges, indecipherable slivers of other photographs, and bits of typography. Saroyan himself might have appreciated as minimalist poetry the text that can be seen on one of the pages visible in Jaws: “re / oy / n- /e- /e- / a” and so on.

Like Baum, Anne Collier is drawn to images that have been put into circulation by being published—and not just in books, but also in magazines, on record covers, and anywhere else. Her May/Jun 2009 (Cindy Sherman/Mark Seliger), from that same year, shows two copies of a magazine cover featuring Sherman, cigarette in hand, a picture taken by a well-known celebrity portraitist. The magazine is L’Uomo Vogue, and it’s funny to see the big black letters l’uomo, “the man,” stretched across the forehead of this prominent woman. Sherman is dressed in a rather butch white shirt, jacket, and tie; with little more than the visual equivalent of a raised eyebrow, Collier seems to be asking us to wonder to what extent a woman has to masquerade as male in order to be successful, as a photographer or anything else.

The image of the female photographer is a recurrent concern for Collier. At the Guggenheim, there’s also Woman With a Camera (Cheryl Tiegs/Olympus I), from 2008. Presumably derived from a camera ad, the work shows Tiegs, a ’70s supermodel, posing as a photographer—except that instead of placing the camera in front of her face and looking through the viewfinder, she’s holding the camera next to it, so the viewer can still see how pretty she is. As this piece shows, Collier is not above scoring an easy point. “In this and similar photos,” Blessing writes in the exhibition catalog, “we are provoked to think carefully about who is taking the picture and why.” Well, not really: The photo is more like an invitation to condescend to the poor fools who could concoct such an image or be taken in by it.

Collier’s work, like a lot of recent rephotography, can feel too clever for its own good, but there’s more to her art than that, as I learned when I saw a retrospective of her work at the Art Gallery of Ontario in Toronto. (Curated by Michael Darling, the exhibition originated at the Museum of Contemporary Art in Chicago.) The show is not free of Collier’s penchant for superciliousness toward her material, a self-congratulatory superiority that’s summed up, for me, in Darling’s discernment of what he calls “a halo of critique” surrounding Collier’s Woman With a Camera pictures. Practicing critique is not a road to beatification, so spare me the halos. More often, however, one senses Collier’s genuine and not unsympathetic bafflement with the strange ways that emotions are manifested in words and images. The 2011 series “Questions” is one of her best: Each of the five photographs shows what seems to be the same manila folder filled with several distressed sheets of paper in a variety of colors. In each of the photos, a different sheet is on top; each has a different heading—“Relevance,” “Supposition,” “Connection,” “Viewpoint,” “Evidence”—and two to four pertinent questions. The page on “Relevance” asks: “~Why is this important? ~What does it all mean? ~Who cares about this idea?,” while the one on “Viewpoint” wonders: “~From whose viewpoint or perspective are we seeing, reading, or hearing? ~Are there other ways to interpret this information?” Are these teaching aids for a creative-writing class or, for that matter, a photography course? Who knows, but the questions that bedevil a beginner still burden the mature artist—and the thoughtful viewer should be asking them too.

Like all of the artists in “Photo-Poetics” and most of those in “Ocean of Images,” Collier pursues an ideal of reflexivity—of photography about photography—that amounts to a contemporary equivalent of the classical unities of 17th-century theater. She strives to knit a work together so tightly—with even any external referent having been definitively incorporated—that it becomes, in its way, self-evident and indisputable. The risk is that if reflexivity becomes too complete, the work becomes nearly facile, self-regarding. Only when it addresses inarticulable feelings or unresolvable questions—as in Collier’s Questions (Evidence): “~How do we know what we know? ~What is the source and how reliable is it?”—does it become (to borrow George E. Lewis’s unforgettable conundrum) a power stronger than itself.