Explore the theory of Anosov representations in this comprehensive lecture, part of a three-part minicourse designed for non-experts. Delve into the construction of domains of discontinuity for Anosov representations and their connection to convex projective geometry. Gain insights from Tengren Zhang of the National University of Singapore as he discusses recent developments and potential research directions in this field. This 65-minute talk, presented at the Institut des Hautes Etudes Scientifiques (IHES), offers a deep dive into a crucial aspect of geometric group theory and dynamical systems.