This thesis studies spherical variants of the Sherrington-Kirkpatrick model for spin glasses, in particular the spiked SSK model and the multiple SSK model with constrained overlaps. The focus lies on the limiting free energy of these models and the proof that it can be expressed in terms of a Thouless-Anderson-Palmer (TAP) variational principle. Furthermore this thesis investigates the fluctuations of the ground state energy of the spiked SSK model.