The present status of particle physics is that the Standard Model has been completed with the discovery of theHiggs boson in 2012, but there is a multitude of phenomena in nature which is not accounted for by this model.Researchers are investigating possibilities for detecting new physics at the current particle physics facilities, withthe Large Hadron Collider (LHC) at the frontier. As no significant sign of new physics has been observed as oftoday, precision phenomenology becomes increasingly important. This thesis and the four papers included in itcontribute to this field of precision predictions for various important processes at the LHC.In paper I and paper IV, the Drell足-Yan process is investigated, and specifically, the decay coefficients whichparameterize the spherical distribution of the outgoing leptons in the process. In the first work, we investigatethe next足-to足-leading足-order (NLO) electroweak corrections to the coefficients of the neutral足-current process. In thesecond work, a similar study, but including also next足-to足-next足-to足-leading足-order quantum chromodynamic (QCD)corrections, is performed for the decay coefficients of the charged-足current Drell足-Yan process. The latter processand the corresponding coefficients are of great importance for measuring the W 足boson mass at the LHC.In paper II, the top quark pair production and the spin correlations for the process are investigated. The spincorrelation information of the top quarks may reveal underlying new physics when probed at high precision.Therefore, this work computes approximate complete足-NLO corrections, including electroweak corrections to thespin correlation coefficients and related leptonic distributions, contributing to the state-足of足-the足-art high precisionStandard Model predictions for these observables.Finally, paper III is the theoretical base of a crucial improvement to matrix-足element generators. We proposein this paper to utilize a next足-to足-leading足-colour truncation of the colour matrix in the large足-Nc limit, in order toreduce the complexity of the cross section computation when a large number of QCD patrons are involved in theprocess. The results suggest that such a truncation of the colour expansion will facilitate for efficient computationof multi-足jet events, which are a dominant background for many important processes and new physics searches athadron colliders, such as the LHC.