Explore the intersection of crosscap states and integrability in this 57-minute conference talk by Shota Komatsu from CERN. Delivered as part of the Talking Integrability: Spins, Fields, and Strings conference at the Kavli Institute for Theoretical Physics, delve into recent advances in integrable models across mathematical physics, condensed-matter physics, and string theory. Gain insights into topics such as integrable deformations of CFTs and IQFTs, integrable spin-chains and their non-equilibrium dynamics, and integrable structures on string worldsheets. Benefit from a comprehensive overview of the field, suitable for integrability practitioners from various backgrounds, as experts come together to bridge gaps between different areas of research.