I will talk about joint work with Andras Vasy defining the Feynman propagator for massive scalar fields on asymptotically flat spacetimes general enough to include radiative perturbations of Minkowski space with no symmetries. The Feynman propagator is an inverse of the Klein-Gordon operator producing solutions which are "positive-frequency" in the future and "negative-frequency" in the past, whose existence and uniqueness does not reduce to a local-in-time problem unlike the advanced/retarded solutions. This condition can be expressed in terms of an appropriate notion of wavefront set, and relevant mapping properties established using the microlocal approach to non-elliptic Fredholm theory. We extend this method, previously also used by Gell-Redman—Haber—Vasy and Baskin—Doll—Gell-Redman, to radiative spacetimes by applying it in a new pseudodifferential algebra developed by Sussman for microlocal analysis on a spacetime compactification with distinct boundaries at spacelike, null, and timelike infinity.