I will give an introduction to the scattering equations, which provide beautiful new formulas for the scattering amplitudes of several theories of massless particles, including gauge theory and gravity. I will start with the basics of the tree-level scattering equations and the new formulas of Cachazo, He and Yuan. Then, I will review how these formulas arise from worldsheet models of field theories inspired by string theory, known as ambitwistor string theories. These models, proposed by Mason and Skinner, are modern realisations of Witten’s idea of gauge theory as a string theory in twistor space. Finally, I will describe the recent success in extending this line of work beyond tree level, leading to interesting new representations of loop integrands in theories with or without supersymmetry.
