Abstract
The notion of conformal infinity grew out of the desire to describe graviational waves in a coordinate independent way. In a sense it abstracts the notion of a far-field in electrodynamics in a geometric way. This contribution describes the development of this idea from the earliest attempts to geometrically capture the notion of gravitational radiation by Felix Pirani to the rigorous definition by Roger Penrose which is universally accepted today. The usefulness of the concept is demonstrated with some applications.