Abstract: Anosov representations extend the class of convex cocompact representations from Lie groups of rank one to higher rank Lie groups as e.g. SL(n,R) or SL(n,C). I will describe a construction of cocompact domains of discontinuity for Anosov representation. Depending on time I will discuss three applications: 1) Realizing higher Teichmueller spaces as deformation spaces of geometric structures, 2) Compactifying proper actions on symmetric spaces, and 3) Constructing compact Clifford-Klein forms of homogeneous spaces. This is joint work with O. Guichard.