We discuss two recent topics on heavy-ion quasi-elastic scattering at energies around the Coulomb barrier. The first topic is an application of quasi-elastic scattering at deep-subbarrier energies to extracting the surface diffuseness parameter of the nucleus-nucleus potential. TheMe second topic is a coupled-channels analysis for the quasi-elastic barrier distribution for the Zn-70 + Pb-208 reaction. We show that the coupled-channels calculations which include the multi-phonon excitations in the colliding nuclei reproduce reasonably well the experimental excitation function for quasi-elastic scattering at backward angles and the barrier distribution for this reaction.