  This talk reviews Feynman integrals, which are associated to elliptic curves.
The talk will give an introduction into the mathematics behind them, covering
the topics of elliptic curves, elliptic integrals, modular forms and the moduli
space of $n$ marked points on a genus one curve. The latter will be important,
as elliptic Feynman integrals can be expressed as iterated integrals on the
moduli space ${\mathcal M}_{1,n}$, in same way as Feynman integrals which
evaluate to multiple polylogarithms can be expressed as iterated integrals on
the moduli space ${\mathcal M}_{0,n}$. With the right language, many methods
from the genus zero case carry over to the genus one case. In particular we
will see in specific examples that the differential equation for elliptic
Feynman integrals can be cast into an $\varepsilon$-form. This allows to
systematically obtain a solution order by order in the dimensional
regularisation parameter.
