Sommerfeld Theory Colloquium, 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.