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Aspects of Supersymmetry after LHC Run I

Supersymmetry is a prime candidate for physics beyond the Standard Model because low-energy supersymmetry stabilizes the Higgs mass avoiding fine-tuning and leads to natural electroweak symmetry breaking. However, searches at the Large Hadron Collider (LHC) for supersymmetric particles have not found any signal and give strong limits on mass of gluino and squark. Also, the observed Higgs mass of 125 GeV is not easily accommodated in the minimal supersymmetric Standard Model (MSSM) where one has to rely on the radiative corrections to boost the Higgs mass accompanied with fine-tuning. I study aspects of supersymmetry in light of these LHC results. In this thesis, I focus on the Compact Supersymmetry model based on arXiv:1206.4993 and the Dirac Next-to-MSSM based on arXiv:1308.0792 and investigate them in more detail.