Abstract: I will describe past and ongoing work on the mysterious relation between periods of motives in algebraic geometry and Feynman integrals in perturbative quantum field theory. I will illustrate two different approaches to this question: a "top-down approach", based on joint work with Connes, that aims at comparing the data of renormalization with mixed Tate motives by relating the Tannakian categories that govern both sets of objects and a "bottom-up approach", developed by Bloch, Esnault and Kreimer, that aims at concretely identifying periods associated to individual Feynman graphs via the parametric representation of Feynman integrals. I will discuss recent and ongoing work with Aluffi on this approach. I will also show how the two different approaches may be combined.