I will review some classical results in twistor theory, the Penrose transform and the non linear graviton theorem, with an emphasis on their interactions and description in terms of the geometry of null infinity. In particular I will try to highlight the role of Newman's H-space in this context.
This presentation will hopefully serve as a starting point for the participants willing to enter the recent literature. Keeping this in mind, and if time permits, I will discuss Adamo-Mason-Sharma's twistor sigma model and the relationship with Lw-infinity symmetries.