  In this talk we discuss a class of Feynman integrals, which can be expressed
to all orders in the dimensional regularisation parameter as iterated integrals
of modular forms. We review the mathematical prerequisites related to elliptic
curves and modular forms. Feynman integrals, which evaluate to iterated
integrals of modular forms go beyond the class of multiple polylogarithms.
Nevertheless, we may bring for all examples considered the associated system of
differential equations by a non-algebraic transformation to an
$\varepsilon$-form, which makes a solution in terms of iterated integrals
immediate.
