Recently, there have been remarkable advances concerning the systematic integration of higher loop Feynman amplitudes. A synthesis of differential equation and number theoretical methods can be employed to calculate position space Feynman amplitudes in the massless case. The combination of these two methods makes this approach very efficient, as an IBP reduction step can be bypassed. We will review on how these techniques were used by one of the authors to calculate the 7-loop beta function in phi^4 theory in D=4. Moreover, we will show how these methods can be extended to general even dimensions and illustrate a further extension to gauge theories.