We consider energy minimizing configurations of a nematic liquid crystal, as described by the Landau-de Gennes model. We focus on an important model problem: a nematic surrounding a spherical colloid particle, with homeotropic anchoring (ie, along the normal vector,) at the surface. For topological reasons, the nematic director must exhibit a defect (singularity), which may take the form of a point or line defect. We consider two physical regimes in which `Saturn-ring' configurations will be energetically favorable: the case of colloids of small radius, and the case of strong applied magnetic fields. This represents work in collaboration with L. Bronsard and X. Lamy.