The work presented in this thesis explores the experimental, phenomenological, astrophysical and cosmological constraints on SUSY models with three distinguished input scales. The SUSY SU(5) GUT model assumes the soft SUSY-breaking parameters to be universal at the GUT scale $M_{\mathrm{GUT}}$. In the Phenomenological MSSM with eleven parameters (pMSSM11), the input parameters are specified at the $\msusy \equiv \sqrt{\mst1 \mst2}$ scale, which is also the scale at which electroweak symmetry breaking conditions are imposed. In the sub-GUT MSSM, the universality of the input parameters is imposed at some input scale $M_{\mathrm{in}}$ below $M_{\mathrm{GUT}}$ but above the electroweak scale. In addition to the SUSY models, this work also includes a global analysis of Dark Matter Simplified Models (DMSMs) with leptophobic spin-one mediator particles with either vectorial or axial couplings to Standard Model (SM) particles and the dark matter (DM) particle. The {\tt MasterCode} tool is used to analyse the constraints on the parameter spaces of each model, taking into account the relevant searches from up to 139/fb of LHC data at $\sqrt{s}=$~13 TeV, and the most recent limits from the LUX, PICO, XENON1T and PandaX-II experiments. Other experimental constraints are also taken into account (when applicable), including those from flavour physics, electroweak precision observables, the anomalous magnetic dipole momentum of the muon, and cosmological constraints on the DM relic density. The DM annihilation mechanisms responsible for bringing the relic density into the allowed region are identified in the preferred regions of the parameter spaces.