I will discuss the integrability and wall-crossing properties of Kondo line defects in rational conformal field theories. It provides a large class of interesting defect RG flow starting from topological line defects. As a surprise, I will discuss new examples of the ODE/IM correspondence and our attempts towards its physical origin using 4d Chern Simons theory. This work is part of a multi-pronged exploration of studying 4D Chern-Simons theory as an overarching structure for integrable systems. ---- Part of London Integrability Journal Club. New participants can register using the form at integrability-london.weebly.com. The link will be emailed.