In this talk, I plan to illustrate the diverse methods I have been employed over the past few years for both analytical and numerical computation of multi-loop scattering amplitudes in quantum and in classical field theory. The first part of my discussion will focus on analytical computations and will provide an overview of the current state of the art. I will introduce integral and integrand reduction methods for efficient calculation of scattering amplitudes. Approaches for analytic computations of Feynman integrals are addressed, underlining current obstacles. Shifting gears in the second part of my talk, I will delve into a fully numerical framework known as the loop-tree duality. Within this context, I will show how stability in numerical evaluation becomes crucial when computing physical observables in four space-time dimensions. Special emphasis will be devoted on the calculation of two-loop electron-muon elastic scattering, and three-loop Higgs plus jet production amplitude.