I discuss a new approach to integrable lattice models and supersymmetric gauge theories, which was motivated by string theory considerations. This approach provides a unified perspective on various important notions, such as the Belavin model, the Jimbo–Miwa–Okado model, the Bazhanov–Sergeev model, Felder's elliptic quantum groups, the vertex-face correspondence, the elliptic modular double, and an elliptic lift of the relation between the chiral Potts model and the six-vertex model. Furthermore, it relates these notions to four-dimensional supersymmetric gauge theories and their surface operators.