  In asymptotically Minkowski space-times, one finds a surprisingly rich
interplay between geometry and physics in both the classical and quantum
regimes. On the mathematical side it involves null geometry, infinite
dimensional groups, symplectic geometry on the space of gravitational
connections and geometric quantization via K\"ahler structures. On the physical
side, null infinity provides a natural home to study gravitational radiation
and its structure leads to several interesting effects such as an infinite
dimensional enlargement of the Poincar\'e group, geometrical expressions of
energy and momentum carried by gravitational waves, emergence of non-trivial
`vacuum configurations' and an unforeseen interplay between infrared properties
of the quantum gravitational field and the enlargement of the asymptotic
symmetry group. The goal of this article is to present a succinct summary of
this subtle and beautiful interplay.
