She is perhaps best known for documenting the New York graffiti scene of the 1970s and '80s. Her most known personal work began while working at the New York Post. On her return home from the Post she began taking photos of children in her New York city neighborhood. One day she met a young kid named Edwin who helped expose her to some of the graffiti around her neighborhood. Edwin helped to explain to her that Graffiti is an art form and that each artist was actually writing his/her nickname. Edwin then proceeded to tell of the Graffiti King and asked if she would like to meet him. This is when Martha met Dondi, the first one who allowed her to accompany him; while Dondi was tagging she would take photos of his art. In the 1980s she put together a book of photos illustrating the Graffiti subculture called Subway Art. She has degrees in art and anthropology.

She was a photography intern at National Geographic Magazine in the 1960s, and worked as a staff photographer at the New York Post in the 1970s. Her photographs have appeared in National Geographic, Smithsonian and Natural History magazines as well as several dozen books and journals. She is the Director of Photography at City Lore, the New York Center for Urban Folk Culture. Cooper lives in Manhattan but is working on a photo project in Sowebo, a Southwest Baltimore neighborhood.

In the 1980's Martha worked briefly in Belize photographing the people and archaeological remains of the Mayan culture. Two sites that received publication in National Geographic were Nohmul & Cuello, both under the direction of Dr. Norman Hammond.