The concept of null-infinity was formulated by R. Penrose in 1962 in order to give a geometric description of asymptotically flat space-times. Since then, this idea has been fundamental in many applications of general relativity, not the least being the rigorous definitions of gravitational radiation and global quantities, such as energy-momentum and angular momentum. In this talk, I will present a different view on the (degenerate) geometric structure of null-infinity, which draws attention to the idea of a cut-system. The interplay between a cut-system and conformal invariance is explored leading to an invariant definition of a Minkowski space-time "at infinity". Some consequences of this structure will be discussed.