Superstring scattering amplitudes in genus one have a low-energy
expansion in terms of certain real analytic modular forms, called
modular graph functions (after D'Hoger, Green, Gürdogan and Vanhove).
I will sketch the proof that these functions belong to a family of
iterated integrals of modular forms (a generalization of Eichler
integrals), recently introduced by Francis Brown, which explains many
of their properties. The main tools are elliptic multiple
polylogarithms (due to Brown and Levin), single-valued versions
thereof (following Schnetz), and elliptic multiple zeta values
(Enriquez).