Twistor strings and supergravity

Einstein gravity can be formulated in such a way that it leads to a perturbation theory about an asymmetric weak coupling limit that treats positive and negative helicities differently. The power counting rules for scattering amplitudes then suggest an interpretation in terms of a twistor string theory for gravity, with amplitudes supported on holomorphic curves in twistor space. After reviewing this formulation, I survey the recent construction of a family of new twistor string theories which are free from world-sheet anomalies and give the space-time spectra of Einstein supergravities, with second order field equations instead of the higher derivative conformal supergravities that arose from earlier twistor strings.