Marton obtained her PhD from Eötvös Loránd University in 1965 and worked at the Department of Numerical Mathematics, Central Research Institute for Physics, Budapest from 1965 to 1973.

Important influences on her early career were her attendance at the combinatorics seminar organised by Alfréd Rényi from 1966, meeting Roland Dobrushin in Debrecen in 1967 (which led to her visiting the Institute for Problems in Information Transmission in Moscow in 1969[3]), and her collaboration with Imre Csiszár which began in 1972.

In a 1974 paper on information theory she used a combinatorics approach to characterize error in discrete memoryless sources under distortion.

a field of characteristic 2 has been posted as a preprint by Tim Gowers, Ben Green, Freddie Manners and Terry Tao.

[11][10] Marton's other major contributions included coding theorems for the broadcast channel[12][13] (with the former paper proving the best-known inner bound on the capacity region of the two-receiver general broadcast channel, often referred to as "Marton's inner bound"[14]) and many other results in concentration of measure,[15][16] rate-distortion theory[17][18] and graph capacity.

As a result, she delivered the Shannon Lecture at the International Symposium on Information Theory in Istanbul in 2013, with her talk being entitled Distance-Divergence Inequalities.

In turn, the Talagrand inequality triggered the development a whole field, which I explored with Otto, McCann, Lott and others, involving entropy, concentration, transport, Ricci curvature, with very far reaching geometric consequences."