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Feynman integrals are ubiquitous quantities in (perturbative) quantum field theory, with applications ranging from condensed matter physics, to collider physics, and even theoretical predictions for gravitational wave production in black-hole scattering. I will review recent developments in their calculation, both with numerical and analytical approaches. These approaches all build on a better understanding of the relations satisfied by Feynman integrals, the type of functions they evaluate to, and the physical properties encoded in their analytic structure.