The universal Teichmuller space consists of all quasisymmetric maps of the circle that fix three points. Following an idea of Bonahon, the universal Teichmuller space embeds into the space of geodesic currents of the hyperbolic plane. Thurston's boundary to the universal Teichmuller space is identified with the space of projective bounded measured laminations of the hyperbolic plane. In a joint work with Hrant Hakobyan, we study the limit points of geodesic rays on Thurston's boundary.