Title: Overview of Classical and Quantum Integrability in Four Dimensions

Abstract: This talk will review recent progress by a number of groups in understanding classical and quantum integrable models in four dimensions. This has been achieved by exploiting twistor methods. After a short introduction to twistors, I will introduce some of the simplest examples of 4d theories with twistor uplifts: self-dual Yang-Mills and the 4d WZW model. I then plan to touch on a number of topics including: the connection to 4d Chern-Simons theory, quantization of these theories on twistor space, their hidden symmetry algebras (also known as celestial chiral algebras) and finally the twistor string.