Geometric structures modeled on homogeneous varieties are studied to characterize homogeneous varieties and to prove the deformation rigidity of them. To generalize these characterizations and deformation rigidity results to quasihomogeneous varieties, we first study horospherical varieties and geometric structures modeled on horospherical varieties. Using Cartan geometry, we prove that a geometric structure modeled on a smooth horospherical variety of Picard number one is locally equivalent to the standard geometric structure when the geometric structure is defined on a uniruled manifold of Picard number one. I will try to talk whole story about this work with some details.