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.