Taryn Simon, Tate Modern, London

The American photographer Taryn Simon is known for her photographs that create unnerving or strange indexes to the world. For a past project she spent five days around the clock at JFK airport photographing seized contraband goods (including guns, hair irons andguinea pig meat). A 2009 work, An American Index of the Hidden and Unfamiliar, saw her photographing places and scenes usually out of sight in America: a labiaplasty, the CIA art collection.

The opening of this new show was attended by a cluster of celebrities including Gwyneth Paltrow (the artist is married to her brother), Steven Spielberg and Cameron Diaz. Glamorous indeed, but Simon's projects are laborious, politically complex and fraught with difficulty. For a Living Man Declared Dead and Other Chapters, which she has been working on for four years, Simon has been photographing the descendents of 18 different bloodlines, each based around a particular situation or narrative that the inheritance somehow expresses. On view are large framed grids of many faces, each individual photographed in front of a flat buff background. There are many blank photographs standing in for those who couldn't be photographed. These grids are accompanied by a group of other photographs (a "footnote" panel) – landscapes and other evocative scenes.

There are 18 of these sets (or "chapters"). The one that gives the work its title is the story of Shivdutt Yadav, of Uttar Pradesh, India, who discovered that he and members of his family had been listed as dead and the ownership of their land transferred to other relations. That they are very much alive has been documented by Simon. Among the images on the footnote panel is something horrific, yet almost beautiful. A body, dead from leprosy floats in the Ganges – the body bleached white, the eyeballs pale and swollen, the face turned black with blood.

Presented in a way that is reminiscent, aesthetically, of encyclopaedias, our eyes are tempted to skim over these images. Individual scenes leap out, however: the floating body described above; an awkward portrait shot; the tightly packed, florally decorated rooms of Ukrainian orphanages. There were moments I wished I was looking at these images separately, perhaps on a larger scale. That they are locked together in a frame is, however, a statement from the artist about the complexity of each situation – the people, the images and stories, cannot be separated from one another.

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