Explore a 51-minute conference talk from the Talking Integrability: Spins, Fields, and Strings conference at KITP, delivered by Stefano Negro from NYU. Delve into the intricacies of integrable models in mathematical physics, condensed-matter physics, and string theory. Discover recent advances in topics such as integrable deformations of CFTs and IQFTs, integrable spin-chains and their non-equilibrium dynamics, and integrable structures on the string worldsheet. Gain insights into the connections between AdS(d+1)/CFT(d) and CFT(2) structures. Benefit from a pedagogical overview of the field, suitable for integrability practitioners from various backgrounds. Examine concepts like quasilocality, ground state motivations, pseudorlink configurations, resonances, bosonic statistics, and central charge. Engage with this comprehensive presentation that brings together researchers from across disciplines to discuss cutting-edge developments in the study of integrable systems.