The development of twistor geometry for the description of fundamental physics

I will review the basic defi�nitions and ideas of the twistor program for fundamental physics, as started by Roger Penrose around 1970. I will give particular attention to certain conformally invariant struc- tures involving deformed helicities, relevant to scattering amplitudes for massless �elds. These played a role in Penrose's earliest contour integral expressions, but have more recently been rediscovered and greatly developed as an approach to regularization.