In this thesis, we assume a minimal supersymmetric extension of the Standard Model (MSSM) with conserved R -parity such that the lightest neutralino is the cold dark matter candidate. A stringent constraint on the MSSM parameter space can be set by the comparison of the predicted neutralino relic density with the e xperimentally determined value. In order to match the high experimental precisio n, uncertainties within the theoretical calculation have to be reduced. One of the ma in uncertainties arises from the cross section of annihilation and coannihilation proce sses of the dark matter particle. In a phenomenological study we investigate the interplay of neutra lino-neutralino annihilation, neutralino-stop coannihilation and stop-stop annihilatio n. We demon- strate that neutralino-stop coannihilation contributes significant ly to the neutralino relic density and is furthermore very well motivated due to the rece nt discovery of a 125 GeV Higgs boson. Due to this ample motivation we have calculated the full O ( α s ) supersymmetric QCD corrections to neutralino-squark coannihilation. We show in detail o ur DR /on-shell renormalization scheme for the treatment of ultraviolet divergenc es, and describe the phase space slicing method which is used to handle soft and collinea r infrared divergences. Further, we comment on the treatment of occurrin g intermediate on- shell states. The whole calculation is provided within the numerical tool DM@NLO that serves as an extension to existing relic density calculators, which consider only an effective tree-level calculation. Based on three example scenarios we study the impact of the NLO corrections on the total (co)annihilation cross section, and o bserve corrections of up to 30 %. This leads to a correction of 5 − 9 % on the relic density, which is larger than the current experimental uncertainty and is, thus, im portant to be taken into account