Modern amplitude methods have made a huge impact on our understanding of quantum field theory and our ability to make precise predictions for physical observables. Their remarkable mathematical structure has led to new results in an enormous range of subjects from gravitational waves, condensed matter systems and collider experiments.

Collider experiments are entering a new era of precision physics. The ongoing Run 3 at the LHC, and the planned High-Luminosity upgrade, will have a significant impact on both systematic and statistical uncertainties of the experimental measurements. The result will be percent level errors for key observables that are highly sensitive to the parameters of the Standard Model. It is therefore of utmost importance to ensure that our theoretical predictions, based on perturbative expansions of production rates, reach a level of precision, which is adequate to make the best use of the wealth of data collected by the LHC experiments. In this respect, amplitude-driven multi-loop computations have become the norm in the theoretical community.

Since the first direct observation of gravitational waves in 2016 by LIGO/Virgo about 100 coalescence events have been collected for a multitude of spin and mass configurations. The discoveries will hugely increase with the next-generation ground-based observatories and the space-borne Laser Interferometer Space Antenna (LISA). Accordingly, in recent years amplitude-driven computations have been applied successfully to obtain precise predictions for gravitational-wave observables.