  This essay was written as an extended version of a talk given at a conference
in Strasbourg on "Riemann, Einstein and geometry", organized by Athanase
Papadopoulos in September 2014. Its aim is to present Roger Penrose's approach
to asymptotic analysis in general relativity, which is based on conformal
geometric techniques, focusing on historical and recent aspects of two
specialized topics~: conformal scattering and peeling.
