Constructing spherical three-dimensional CR-manifolds

It seems that a vast majority of known closed 3-manifolds admitting a spherical CR-structure are Seifert fibered spaces (however, there are sporadic exceptions). I will present a couple of approaches to constructing such 3-manifolds. They are based on papers by Goldman–Kapovich–Leeb, Anan'in–Grossi–Gusevskii, and some yet unpublished work, e.g., by Carlos H. Grossi.