Even after the discovery of a Higgs boson fundamental questions of particle physics remain unanswered. Neither the origin of the baryon-antibaryon asymmetry of the universe, nor the nature of Dark Matter is understood. Two models of New Physics capable of addressing these problems are investigated here. In the first part of the thesis branching ratios for the decays of the lightest up-type squark in the Minimal Supersymmetric Extension of the Standard Model (MSSM) are calculated to high precision for scenarios with compressed supersymmetric spectra by including the finite width of the $W$ boson. These branching ratios affect the limits on the model which can be set by experiments. The second part concentrates on predictions of cross sections for squark gluino production in the MSSM. Spin correlations between the production and the decay of the gluino as well as next-to-leading order corrections are taken into account and a framework consistently treating both the production and the decay of the squark and the gluino in an event generator is elaborated. First results show that the impact of spin correlations on differential cross sec ... mehrtions is considerable. In the last part the electroweak phase transition is investigated in the Two-Higgs-Doublet Model by analyzing the loop-corrected effective potential at finite temperature. Based on the development of a new renormalization prescription an effective scan over the parameter space of the model is performed. The results show that demanding a strong first order phase transition, as required for baryogenesis, leads to strong constraints on collider observables.