Appears in collection : Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups

We will review some dynamical systems associated to an Anosov representation and draw some geometric conclusions. More precisely, we will review topics such as the Patterson-Sullivan Theory for these representations, the critical hypersurface, dynamical intersection, dynamics of the \theta-Weyl-chamber flow, and finally directional-conicality and generalizations. We will then consider the approach of dominated sequences and draw conclusions on the regularity of limit sets. Some relevant references are lecture 1: Babillot-Ledrappier, Bridgeman-Canary-Labourie-S., Burger-Landesberg-Lee-Oh, Carvajales, Chow-Sarkar, Dey-Kapovich, Ledrappier, Lee-Oh, S. lecture 2: Bochi-Potrie-S., Pozzetti-S., Pozzetti-S.-Wienhard, Zhang-Zimmer.