DescriptionIn this thesis we explore different aspects related to the central concepts of supersymmetry and physics beyond the Standard Model. We start by investigating fine-tuning in the minimal supersymmetric extension of the Standard Model, where the regions with the minimal amount of fine-tuning of electroweak symmetry breaking are found. Afterwards, we concentrate on a more formal aspect of supersymmetry, studying spontaneous symmetry breaking in supersymmetry using the superspace formalism. Thereafter we direct our attention to supersymmetry as physics beyond the Standard Model, looking more specifically at supersymmetry breaking in metastable states. First, we discuss possible undetected Higgs decays in the Pentagon model with renormalizable lepton number violating couplings which also explain neutrino masses. Second, we generalize metastable supersymmetry breaking in supersymmetric quantum chromodynamics to phenomenologically viable models of direct gauge mediation by adding single and multitrace deformations. Third, we introduce a new model of physics beyond the Standard Model, the Pyramid Scheme, and study its implications, focusing on dark matter and its astrophysical signatures in particular. Four, we examine tunneling constraints in models of Cosmological Supersymmetry Breaking, arguing that these models can have no supersymmetric vacuum states in the infinite Planck mass limit. Finally, we present a general study of the possible gamma ray signatures coming from dark matter annihilation or decay.