Explore the fundamental challenges of identifying and characterizing integrability in discrete dynamical systems through this one-hour lecture by Ralph Willox. Delve into the mathematical complexities that arise when attempting to detect integrable structures in discrete systems, examining the theoretical frameworks and methodologies used to define integrability in non-continuous settings. Learn about the key differences between continuous and discrete integrable systems, the various approaches to testing for integrability, and the ongoing research challenges in this specialized field of mathematical physics. Gain insights into the current state of knowledge regarding discrete integrable systems and the open problems that continue to drive research in this area.