Explore the dynamics of entanglement in monitored quantum processors through this 42-minute conference talk by Michael Gullans from NIST/Maryland. Delivered as part of the Noisy Intermediate-Scale Quantum Systems: Advances and Applications conference at the Kavli Institute for Theoretical Physics, delve into cutting-edge research on integrable models in 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 in various contexts. Gain insights from this pedagogical overview suitable for integrability practitioners across different backgrounds, bringing together diverse perspectives from the field.