Abstract
In the past decades and especially the last one, powerful new tools and remarkable new structures for perturbative scattering amplitudes in QFT have been discovered.
Apart from playing a prominent role in high-energy particle physics, these developments have important implications for a wide range of subjects: from string perturbation
theory to multi-loop calculations in (super)-gravity, from new mathematics to all-loop amplitudes in N=4 SYM. I will review some recent progress, focusing on two
topics: (1) a string-inspired new formulation for amplitudes in gauge theories and gravity, and "double-copy” between them (2) new geometric structures underlying amplitudes
which may hint at a "theory at infinity” for S-matrices.