In this talk, I will recall the notions of C*- and W*-superrigidity for groups. I will then present examples of non-amenable groups that can be completely reconstructed from their reduced C*-algebras, but not from their group von Neumann algebras. These groups are constructed as infinite direct sums of amalgamated free product groups and provide the first known examples of non-amenable groups exhibiting this behavior. This is joint work with Juan Felipe Ariza Mejía and Ionut Chifan.