DescriptionIn this thesis, we study di erent topics relating to supersymmetry at electroweak scale using naturalness and minimality as our guiding principles. We will discuss a new mechanism to generate large A-terms in MSSM. This mechanism could be combined with gauge mediation supersymmetry breaking mechanism to explain the MSSM spectrum and the Higgs mass with minimum ne-tuning. Moreover, we will show that these models may have unique spectrum with one of the stops much lighter than other colored particles. We will also discuss how simple vector-like extensions of MSSM can explain the dark matter relic abundance and the Higgs mass in a natural setting. Among other results, we emphasize a tight relation between relic abundance and spin dependent cross-section in our model. Finally we discuss the e ect of D-term on the vacuum structure of O'Raifeartaigh models and its possible role in models of direct gauge mediation.