Explore a comprehensive lecture on integrable sigma models at renormalization group fixed points, focusing on their quantization as affine Gaudin models. Delivered by Joerg Teschner from DESY/Hamburg, this talk is part of the "Talking Integrability: Spins, Fields, and Strings" conference held at the Kavli Institute for Theoretical Physics. Delve into recent advances in integrable models across mathematical physics, condensed-matter physics, and string theory. Examine topics such as integrable deformations of CFTs and IQFTs, integrable spin-chains and their non-equilibrium dynamics, and integrable structures on string worldsheets. Gain insights into the relationship between AdS/CFT correspondence and CFT structures in two dimensions. Benefit from a pedagogical overview of the field, suitable for integrability practitioners from various backgrounds, as the lecture aims to bridge gaps between different research areas in this domain.