Feynman integrals are indispensable for precision calculations, not only for high-energy particle physics experiments, but also for example for QED precision experiments at lower energies or precision studies in gravitational wave physics. In recent years there has been a significant progress in our abilities to compute Feynman integrals, revealing a rich and fascinating mathematical structure, relating Feynman integrals to (algebraic) geometry. In this talk I will review these recent developments.