LHC Phenomenology of Supersymmetric Models

In this thesis we will study two models of gauge mediation and the phenomenology related to them, keeping the eyes wide open on the possible outcomes for such models at colliders. The first model is a model of Tree Level Gauge Mediation that was firstly proposed in 2009 [50,51] and then extended and more deeply studied recently. In chapter 2 we will discuss the model in its general theoretical realization, while we will devote chapter 3 to the phenomenological realization of its simplest SO(10) realization at the LHC [52] and chapter 4 to the extension of the model to the exceptional symmetry groups case [53]. Then in chapter 5 we will discuss a brand new model of Yukawa-Gauge Mediation analyzing both the theoretical features of the framework and its phenomenology [54]. We will conclude this work through summary and conclusions in chapter 6. The original contribution of the thesis is contained in chapters 3, 4 and 5.