| In the first part of this thesis, dynamical supersymmetry breaking is studied in de-tails. General conditions of supersymmetry breaking for calculable theories are discussed, with emphasize on relation between supersymmetry and R-symmetry. We reviewed the N= 1 SQCD theories including Seiberg duality, and dynamical supersymmetry breaking in these theories induced by nonperturbative effects. As an application of Seiberg duality to supersymmetry phenomenologies, a set of R-symmetric models with Dirac gauginos are explored. In the second part of this paper, a general formalism of calculating soft terms in gauge mediation is discussed, which is also valid nonperturbatively. The information of Higgsed gauge symmetries beyond standard model gauge group can be uncovered by studying their contributions to the soft masses. For illustration, sum rules of soft terms in an extra abelian gauge group and non-abelian supersymmetric left-right models are dis-cussed respectively. Also we discussed a set of light hidden sector known as hidden valley in framework of general gauge mediation. In the last part of this paper, nonlinear realiza-tions of supersymmetry and low energy effective field theory of goldstino are reviewed. We prove that the Seiberg's new proposal can be rephrased via the languages of standard nonlinear realization.
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