In this talk I will discuss how underlying algebro-geometric structures characterise Feynman amplitudes as periods of motives and how techniques in algebraic geometry are applied to the motivic version of amplitudes to give information about their numerical value. I will give particular attention to the application of motivic Galois theory to Feynman diagrams of primitive log-divergent type in $\phi^4$ quantum field theory. This talk is based on arXiv:2009.00426.