The computation of Feynman integrals is an important ingredient to compute scattering amplitudes to higher orders in perturbative QFT. Over the last couple of years, a lot of progress was made in understanding the mathematics of multi-loop Feynman integrals. In particular, it was understood that large classes of integrals evaluate to a class of special functions called multiple polylogarithms, which are an object of active research also in pure mathematics. It is known that starting from two loop, generalisations of polylogarithms to elliptic curves can show up. In this talk we review certain classes of elliptic multiple polylogarithms, and we show that they are closely related to iterated integrals on certain modular curves.