This research focuses on top-quark physics. The top quark is the heaviest elementary particle known to date and this property has remarkable consequences, which provides enough motivation for detailed studies. The aim of this dissertation is to perform such studies, as briefly described below, at the highest possible level of accuracy and precision in order to fully exploit the experimental information. The precise determination of the top-quark properties is essential for the SM, and for this, one has to study the top-quark processes. The first part of this study is concentrated on the top-quark pair production at the LHC. This process is very accurately measured and provides the ideal environment for detailed comparisons between theory and data. NNLO QCD and NLO EW calculations are combined in order to provide the most accurate prediction for this process at cross section and differential level at 13 TeV. The second part investigates the top-quark pair production in association with a Higgs boson. It is analysed as a tree level probe of the top Yukawa, along with the irreducible backgrounds. These processes are studied at 13 TeV and part of the results is extrapolated to a future 100 TeV collider. In the last part the research is focused on the top-quark pair production in association with a Z boson or a photon. They are studied by parametrizing the top-quark neutral couplings with 6-dim EFT operators. Possible deviations from the SM are explored and the sensitivity of this set of operators is studied in various processes.