Witten's twistor-string theory led to a revolution in the study of scattering amplitudes with remarkble new formulae for tree amplitudes. More recently this theory has been seen as but one example of a large family of string theories, theories of chiral or holomorphic strings in ambitwistor space, the space of complex null geodesics. These theories underpin the recent remarkable formulae of Cachazo, He and Yuan, that encode the tree S-matrices of a variety of quantum field theories in terms of the scattering equations. This talk will review these theories, the CHY formulae, and their extension to loops, and curved space-time.