I will present a modification of the Berkovits twistor string model which gives Einstein supergravity coupled to Yang-Mills, and has a limit in which the gravity modes can be decoupled to give pure gauge theory amplitudes. I will start by reviewing a number of relevant aspects of twistor theory, including special features associated with different space-time signatures, supertwistor space, the Penrose transform, the infinity twistor and Penrose's non-linear graviton construction. I will then review the Witten and Berkovits twistor strings, with emphasis on the latter. The world-sheet formulation of the Berkovits model involves so-called beta-gamma systems, I will describe the symmetries of such systems and their gauging, and explain how the analysis can be applied to the construction of a family of new gauged Berkovits twistor strings which are free from world-sheet anomalies. I will also describe the corresponding spectra in space-time, and show that they give Einstein supergravities instead of the higher derivative conformal supergravities arising in the original twistor string models. The new theories include one with the spectrum of N = 8 supergravity, two theories with the spectrum of N = 4 supergravity coupled to N = 4 Yang-Mills, a family of N greater than 0 models with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills, and a non-supersymmetric string with the spectrum of self-dual gravity coupled to self-dual Yang-Mills and a scalar. Time permitting, I will discuss what is known about the interactions.