  We obtain the total impulse in the scattering of non-spinning binaries in
general relativity at fourth Post-Minkowskian order, i.e. ${\cal O}(G^4)$,
including linear, nonlinear, and hereditary radiation-reaction effects. We
derive the total radiated spacetime momentum as well as the associated energy
flux. The latter can be used to compute gravitational-wave observables for
generic (un)bound orbits. We employ the ("in-in") Schwinger-Keldysh worldline
effective field theory framework in combination with modern "multi-loop"
integration techniques from collider physics. The complete results are in
agreement with various partial calculations in the Post-Newtonian/Minkowskian
expansion.
