Taryn Simon: the woman in the picture

In person, Taryn Simon seems like an unlikely contender for the title of most important photographer of her generation. Dressed in brown woolly tights and a matching check dress that looks thrift shop but is probably designer-Amish, she appears to have stepped out of a Sofia Coppola adaptation of an Edith Wharton novel.

She is charming and personable but becomes palpably nervous when talking about her work, which is characterised by its complexity and ambition. "I do seem to try to make things harder and harder for myself," she says, laughing. "In some perverse way, obstacles interest me and I'm drawn to projects that end up being incredibly laborious."

This week, an exhibition of new work entitled A Living Man Declared Dead and Other Chapters opens at Tate Modern, a rare accolade for a photographer who is just 36 years old. It is an investigation into the nature of genealogy and its consequences and is her most complex, ambitious and laborious project yet. It comprises a series of 18 family bloodlines, each with a strange or arresting individual story at its heart: an Iraqi man who was apparently employed as Saddam Hussein's son's body double; a member of the Druze religious sect in Lebanon who believes in reincarnation and re-enacts remembered scenes from previous lives; a living Indian man who gives the project its title, having been declared dead in official records.

"It is a complex and multilayered exhibition, but also direct and engaging," says Simon Baker, Tate Modern's curator of photography. "There are a small number of photographers who combine the visual and the textual so powerfully, and whose work is sophisticated in terms of contemporary art practice but also hard-wired to the real world. Taryn is certainly one of them. In one way, walking into the exhibition is like entering an incredible book."

Simon is currently one of the hottest properties on the international art photography market. Her prints fetch stellar prices at auction and have been acquired by leading institutions such as the Museum of Modern Art and the Whitney in New York, the Getty Museum in Los Angeles and the Pompidou Centre in Paris, as well as the Victoria and Albert Museum and Tate Modern in London. She is represented by Larry Gagosian, the gallery owner and art dealer who also represents Damien Hirst in New York and oversees the estate of Andy Warhol. A Living Man Declared Dead is on loan to Tate Modern from Jane and Michael Wilson, a couple who are perhaps the most important collectors of photography in Britain. (Michael Wilson, who made his fortune co-producing James Bond films with his sister, Barbara Broccoli, was recently described in the FT as "a one-man Photography Council".)

Socially, too, Simon is well connected. She lives in downtown Manhattan with her husband, Jake Paltrow, a film-maker who recently directed his older sister, Gwyneth, in his debut feature, The Good Night. In an article about their purchase of a $2m apartment in the Village, the New York Observer dubbed them "a dandy 30-ish power couple". When I mentioned her to a New York-based photographer last week, he said, with a perhaps understandable mixture of bemusement and envy, "How many photographers have Steven Spielberg come to an opening?"

For all that, Simon is undoubtedly a serious and committed artist whose work is unapologetically cerebral. She is meticulous, perhaps even obsessive, in her preparation and research. A Living Man Declared Dead took four years to come to fruition, but only about two months of that time was spent photographing the subjects.

"The majority of my work is about preparation," she says during a break from overseeing the installation of her show at Tate Modern. "The act of taking photographs is actually a very small part of the process. I work with a small team, just my sister (Shannon Simon) and one assistant (Douglas Emery). We deal with translators, fixers, fact checkers and the logistics of setting up shoots in places where people do not have the internet or access to telephones. Then there was the actual bloodlines which had to be constructed and verified." She sighs and shakes her head. "It is easily the most difficult and demanding project I have done thus far."

She made her name with An American Index of the Hidden and Unfamiliar, published in 2007, a book that delves deep into a secret America in images that are often both detached and ominous: a nuclear waste storage facility in Washington State; a cryopreservation unit where bodies are frozen just after death; a bio-containment laboratory where deadly animal diseases are studied; a death row outdoor recreational cage; a cave where a sleeping black bear and its cubs are monitored by biologists studying hibernation.

Like an Annie Leibovitz of the conceptual world, Simon seems to possess considerable clout when it comes to both access and control. Her mixture of tenacity and charm seems to have worked wonders on organisations not known for their openness: the Church of Scientology, the Ku Klux Klan and the Prisoner of War Interrogation Resistance Programme run by Team Delta, a private body run by former US military personnel. (Ironically, one of the few organisations that denied her access was Disney, whose spokesperson sent her a fax that read: "Especially during these violent times, I personally believe that the magical spell cast on guests that visit our theme parks is particularly important to protect, and helps to provide them with an important fantasy they can escape to." It was, she told Interview Magazine, "better that any photograph I could have ever produced".)

An American Index of the Hidden and Unfamiliar is one of those rare photography books that struck a chord with both photography buffs and the wider public. In his introduction, Salman Rushdie pinpointed why: "In a historical period in which many people are making such great efforts to conceal the truth from the mass of the people, an artist like Taryn Simon is an invaluable counter-force. Democracy needs visibility, accountability, light… Somehow, Simon has persuaded a good few denizens of hidden worlds not to scurry for shelter when the light is switched on, as cockroaches and vampires do, but to pose proudly for her invading lens…"

Simon grew up in New York and started taking pictures as a child. "Both my father and grandfather were avid photographers. I was introduced to the larger world and photographic production through their slideshows. I would often go on little expeditions with them, taking photographs in a very loose form."

Her father worked for the government, often travelling "to dangerous and distant places and returning with an enormous number of photographs". Her grandfather lived in Connecticut, where he ground glass for telescopes and, as she put it, "was more interested in the macro – stars, insects, and plant and animal life". He also built telescopes, which may help explain the scientific undertow in her current work: the interest in genetic mapping and patterning, the portraits that are presented in systematic grids, complete with footnotes and ancillary information.

Photography, then, is in her blood, though she studied environmental science at college, obtaining a BA at Brown University in Providence, Rhode Island. "I just kept on taking photographs throughout my time there, and afterwards I worked as an assistant for photographers involved in various approaches – anything from a journalist to a toy catalogue photographer. Anything, really, just to learn about lighting and composition and the whole technical side of photography."

After starting out on her own, she did some editorial work for the New York Times magazine before successfully applying for a Guggenheim grant for a tentative work-in-progress that eventually became her first book, The Innocents. Published to considerable acclaim in 2003, it set the tone in both its scope and ambition for much of what was to follow. In large format portraits and extended texts, The Innocents documents American victims of miscarriages of justice, various men – and just one woman – who have served time for violent crimes they did not commit.

Its subtext is photography's role, even complicity, in the wrongful convictions, most of which were often obtained through the police's use of photographs, Polaroids and mugshots of the accused in witness corroboration. "The Innocents is very much about the use and misuse of photography, " says Simon. "I would often take the subjects back to the scene of the crime, a scene that they had never before been to, but were forever linked to. The place that had changed their lives forever. Like some of the chapters in A Living Man Declared Dead, The Innocents is about people suddenly caught up in a narrative that is not their own."

Until she undertook A Living Man Declared Dead, Simon's work was, as she puts it, "about issues of power, mainly American power, at a historical moment when governance and power structures are destabilising and changing due to unpredictable forces like the global economy, environmental changes and asymmetrical warfare". For all that, though, she rejects the label "political artist" and its connotations.

"The work eludes that kind of categorisation intentionally, though, of course, it may activate something political in the viewer or resonate with them in a political way. But I don't have an agenda. I guess a lot of what I do is underpinned by anxiety. But I am also anxious about photography and its role. I try to keep a clear distance from the subject. I never want to say that I understand or somehow know the subject. In fact, it's more that I don't know."

Last year, Simon published Contraband, a book of relatively humble ambition, for which she spent four days without sleep at the US Customs and Border Protection site and the US Postal Service international mail facility at JFK airport in New York. The book is another visual inventory, this time of 1,075 seized items, some bizarre (deer penis, cow dung toothpaste, a dead bird), some mundane (sausages, spices, pumpkins).

"People imagine customs officers seizing familiar threats – drugs or weapons – but most of the seized items were, of themselves, incredibly mundane. I was fascinated by the idea that a banal thing like a banana or an apple could suddenly assume a threatening identity because it is in the contraband room."

In both her creative ambition and conceptual reach, Simon is at the vanguard of a relatively new kind of photography that evades easy categorisation and often blurs the boundaries between reportage, conceptualism and portraiture. Alongside the likes of Jim Goldberg, winner of this year's Deutsche Börse prize, and Paul Graham, whose work is currently on show at the Whitechapel Gallery, she makes work that straddles the worlds of documentary photography and fine art.

"A Living Man Declared Dead is a really important work because it draws on various often exclusive traditions," says Simon Baker. "It has the tenacity we associate with photojournalism and the practices and presentation of art photography. In a way, it's bringing the real world – politics in the broadest sense – into galleries and museums. That is not an easy thing to do, but photography can do it very well and this particular show is an amazing example of a complex and ambitious project that contains within its presentation all the things you need to understand about it."

That may well be so, but I also suspect that, for the casual or curious viewer, it may prove a demanding, even frustrating, experience, not least because the ambition and complexity of the idea almost overwhelms the actual work on the walls – a dilemma that is at the heart of much high-end conceptual art. In one way, too, Simon's work also refutes the long held notion that a great photograph should speak for itself, much of its impact resting on the interrelation of image and text, the latter giving the former much of its power and resonance.

With A Living Man Declared Dead, she has arrived at a place where, visually, all extraneous style and embellishment, even context, has been discarded. The portraits that make up each individual bloodline are arranged in grids and are unadorned and undramatic. They have a certain cumulative power but certainly do not possess the intrigue or the mystery of the images in An American Index of the Hidden and Unfamiliar. This, it turns out, is intentional.

"I think I've just gotten tired of photography in a way," she says, revealingly, at one point, "and am trying to use it as a simple recorder allowing the construction of collections and associations that disturb the value of the single image and underscore issues of translation. Certainly the progression of my work has very much been a shedding of style and embellishment. The neutral background of the non-place behind many of my subjects corresponds to this erasure."

The neutral portraits of individual bloodlines, arranged in scientific grids against white backgrounds, and hung in a huge gallery space where, at Simon's insistence, the walls are ultra-white and the lighting ultra-bright, are punctuated by blank spaces that represent the missing, the dead or those who refused to have their photograph taken. This is a project, then, as these absences attest, about the limits of photography – a strange place for a young photographer to end up. It will be interesting to see where she goes next.

A Living Man Declared Dead and Other Chapters is at Tate Modern, London, 25 May to 6 September. An accompanying book of the work is published by MACK , at £80