When studying the integrands appearing in one-loop closed string amplitudes, one naturally encounters objects called ``(elliptic) modular graph forms''. These were first studied in their infinite sum representation. They can however be expressed as iterated integrals over modular forms which makes the wealth of relations among them manifest.In this representation they give rise to modular and single-valued combinations of such iterated integrals.
During my talk I will first briefly introduce (elliptic) modular graph forms, then review the single valued construction for multiple polylogarithms (relevant for genus zero string amplitudes) to later discuss our results concerning the construction of single valued elliptic multiple polylogarithms (relevant for genus one string amplitudes).Furthermore I will give some possible applications of our results to twisted cohomology and KLT-like relations.