String polytopes are generalizations of Gelfand--Zeitlin polytopes that were introduced by Littelmann and Berenstein--Zelevinsky for semisimple algebraic groups and their highest weight representations. Due to work of Caldero these polytopes induce toric degenerations of flag and Schubert varieties. I will report on joint work with Fourier where we show in type A how string polytopes arise from the cluster structure of the flag variety. More precisely, we show that string polytopes are unimodularly equivalent to tropicalizations of Gross--Hacking--Keel--Kontsevich's superpotential.