I discuss new techniques that can be used to compute multi-loop multi-leg Feynman integrals.
Feynman integrals are generically expressed in terms of multiple polylogarithms and generalizations thereof.
I review the symbol calculus, a tensor calculus that associates to each multiple polylogarithm a tensor over a certain space of functions.
This tensor calculus embodies conjecturally all the functional equations among multiple polylogarithms, and therefore provides an effective way
to simplify analytic results, revealing a sometimes unexpected simplicity for complicated Feynman integrals and scattering amplitudes.
