This thesis provides a detailed account of the legacy of the LHC Run 1 in relation to the Higgs Boson, Supersymmetry, and Dark Matter. The LHC Run 1 was a milestone in particle physics, leading to the discovery of the Higgs boson, the last missing piece of the so-called "Standard Model" (SM), and to important constraints on new physics, which challenge popular theories like weak-scale supersymmetry.First, the SM and the need for its extension are presented in a concise yet revealing way. Subsequently, the impact of the LHC Higgs results on scenarios of new physics is assessed in detail,...