Initially working independently, they finally met, combined their work and published a book called Subway Art in 1984, a tome that was to define the era, and arguably ensure the genre lived on to be reborn as part of the global art movement decades later.
By the end of the 80s, the graffiti culture was being forced to adapt, as by then, New York's Transit Authority had brought in procedures that made it tougher to gain access to the train yards. New models with coatings that were resistant to paint, and faster cleaning of any that were covered in graffiti also meant the artists' work was short-lived and the thrill of seeing the work trundling around the city was lost.
In the years since, some of the artists have fared well in the US and Europe, others have spent time in prison, one has become a policeman and some have died.
The art itself is now part of the mainstream, no longer reserved for city walls but a regular part of a designer's armoury.
For Cooper, the graffiti work is an important part of her time in New York, producing the images she is most proud of, rather than those shot on assignment for newspapers or magazines.
At times, she would spend hours waiting and watching, for that moment when good light combined with a powerful piece of art passing through an interesting part of the city.
Chalfant approached the graffiti from a different angle, concentrating on the work itself, often shooting a series of overlapping images using the motor drive on his camera. He would then splice the pictures together in his studio. He said at the time: "I was more interested in capturing the beautiful, ephemeral work of art than in taking a beautiful picture as a photographer."
Here is a selection of the photographs by Cooper and Chalfant.
Subway Art by Martha Cooper & Henry Chalfant is published by Thames & Hudson.

Karl and Donovan Demetrius, both 29, Jaydene Parsons, 23, and James Ireland, 23, were charged with assisting an offender earlier.
All were remanded in custody after a short hearing at Bristol Magistrates' Court.
Becky's stepbrother, Nathan Matthews, 28, appeared in court earlier charged with her murder.
Karl and Donovan Demetrius, and Ms Parsons, all of Barton Court, Bristol, and Mr Ireland, from Avonmouth, will appear at the city's crown court on 26 March.
They all face a single charge of disposing or concealing Becky's body parts with the intent "to impede the apprehension or prosecution of Nathan Matthews".
A fifth person - a 23-year-old man also arrested on 2 March - was released without charge.
The 16-year-old's stepbrother, of Warmley, Bristol, appeared at the city's crown court via video link earlier, charged with her murder.
He was also remanded in custody to appear at crown court on 26 March.
Mr Matthews' girlfriend, Shauna Hoare, 21, appeared alongside him at Bristol Magistrates' Court on Thursday charged with perverting the course of justice.
She will appear before the crown court on 2 April.
Becky was last seen on 19 February and was reported missing the following day.
The discovery of her body came after an extensive search of various locations across Bristol.
In the late 1970s and early '80s, photographers Martha Cooper and Henry Chalfant were both documenting the work of graffiti artists on the subway system of New York.
[NEXT_CONCEPT]
Four people have appeared in court accused of helping to hide or dispose of teenager Becky Watts' body parts.