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This paper is the fourth in a series dedicated to the mathematically rigorousasymptotic analysis of gravitational radiation under astrophysically realisticsetups. It provides an overview of the physical ideas involved in setting upthe mathematical problem, the mathematical challenges that need to be overcomeonce the problem is posed, as well as the main new results we obtain in thecompanion paper [KM24].  From the physical perspective, this includes a discussion of howPost-Newtonian theory provides a prediction on the gravitational radiationemitted by $N$ infalling masses from the infinite past in the intermediatezone, i.e. up to some finite advanced time.  From the mathematical perspective, we then take this prediction, togetherwith the condition that there be no incoming radiation from $\mathcal{I}^-$, asa starting point to set up a scattering problem for the linearised Einsteinvacuum equations around Schwarzschild and near spacelike infinity, and weoutline how to solve this scattering problem and obtain the asymptoticproperties of the scattering solution near $i^0$ and $\mathcal{I}^+$.  The full mathematical details are presented in the companion paper [KM24].

The Case Against Smooth Null Infinity IV: Linearised Gravity Around Schwarzschild -- An Overview