Supersymmetric gauge theories in four dimensions have various interrelated connections to quantum integrable systems. I will present a new correspondence which identifies Wilson-'t Hooft lines in N=2 circular quiver theories with transfer matrices of trigonometric systems. I will explain how this correspondence is related to Costello's 4d Chern-Simons theory and other similar correspondences. This is based on my joint work with Kazunobu Maruyoshi and Toshihiro Ota. -------------------- Part of the London Integrability Journal Club. New participants please register using the form at integrability-london.weebly.com.