In this thesis, we study spontaneous supersymmetry (SUSY) breaking and its mediation from various perspectives. We begin by motivating SUSY from both phenomenological and more theoretical points of view. After undertaking a brief review of the structure and history of SUSY, we move on to study gauge-mediated SUSY breaking.;We further develop a general formalism for describing the soft parameters generated in theories of gauge mediation. Using this formalism we give a general proof of the finiteness of the soft parameters. Then, specializing to weakly coupled models, we shed new light on the UV sensitivity of the soft masses. Finally, we prove that the parameter space described by our formalism is physical and realizable in calculable, weakly coupled models. This result opens up the possibility of completely new soft spectra not typically associated with gauge mediation.;Next, we make contact with string theory and realize a supersymmetric extension of the Standard Model as the low energy theory of a D3 brane probing a del Pezzo singularity in a gravitational decoupling limit we describe. More importantly, we formulate new topological conditions under which the abelian gauge bosons of the D3-brane theory are rendered massive upon UV completing the singularity into a compact manifold.;Shifting our focus to SUSY breaking in hidden sectors, we analyze how to generate metastable SUSY breaking quantum field theories in string theory. We give a simple set of geometrical conditions for understanding the resulting gauge theory.;In the last part of the thesis, we will introduce a novel string theoretical scheme for mediating SUSY breaking using D-brane instantons.
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