  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. The second topic is a
coupled-channels analysis for the quasi-elastic barrier distribution for the
$^{70}$Zn + $^{208}$Pb 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.
