The Vlasov–Poisson system describes the evolution of an ensemble of either: Electrically charged particles, interacting via an electrostatic Coulomb force; Self-gravitating particles, interacting via a Newtonian gravitational force. In 3 space dimensions, for isolated systems, dispersive solutions asymptotically exhibit logarithmically corrected linear behaviour, i.e. such solutions “scatter’’ in a modified sense (in contrast to 4 space dimensions and higher, where such solutions asymptotically behave linearly). I will discuss a new proof of well posedness of the inverse modified scattering problem: for every suitable scattering profile, there exists a solution of Vlasov–Poisson which disperses and scatters, in a modified sense, to this profile. Further, as a consequence of the proof, the solutions are shown to admit a “polyhomogeneous expansion’’, to any finite but arbitrarily high order, with coefficients given explicitly in terms of the scattering profile. I will then discuss a generalisation to the study of the electromagnetic radiation created by a collection of infalling particles in the context of the Vlasov–Maxwell system. This is joint work with Volker Schlue (Melbourne).