The all-order structure of scattering amplitudes is greatly simplified by the use of (generalized) Wilson line operators, describing (subleading) soft emissions from straight lines extending to infinity. We discuss how these techniques, originally developed for QCD phenomenology, can be naturally applied to gravitational scattering. At the quantum level, we find a convenient way to derive the exponentiation of the (subleading) graviton Reggeization. At the classical level, the formalism provides a powerful tool for the computation of observables relevant in the gravitational wave program.