The main result of this master thesis is the classification of Lorentzian Spin0 manifolds carrying real Killing spinors, previously attempted by Bohle and Leistner. This is obtained as a consequence of the general theory of Psuedo-Riemannian manifolds carrying a closed and conformal vector field, previously developed by Rademacher, Kühnel, Gutiérrez, Olea and others. We further develop this by giving improved statements without any type of completeness assumptions. These results are then carried over to some Pseudo-Riemannian manifolds carrying generalized Killing spinors. We also use the abovementioned theory to give conditions when a Pseudo-Riemannian Spinc,0 manifold carrying a generalized Killing spinor has a specific type of covering. Furthermore, we improve results by Groβe and Nakad concerning imaginary generalized Killing spinors in the Riemannian Spinc case. As a consequence, we finally generalize Baum's classical result concerning imagniary Killing spinors on Riemannian manifolds to the Spinc case.