Recent developments from Feynman integrals

This talk reviews recent developments in the field of analytical Feynman integral calculations. The central theme is the geometry associated to a given Feynman integral. In the simplest case this is a complex curve of genus zero (aka the Riemann sphere). In this talk we discuss Feynman integrals related to more complicated geometries like curves of higher genus or manifolds of higher dimensions. In the latter case we encounter Calabi-Yau manifolds. We also discuss how to compute these Feynman integrals.