In this thesis the Next-to-Next-to-Leading Order (NNLO) perturbative QCD corrections to Z boson production in association with hard QCD radiation are considered, both where the hard QCD radiation forms an observable jet and where no jet definition is required. The Infrared (IR) divergences are regulated using the antenna subtraction method and all possible initial state configurations and colour contributions are considered. This research is the first complete NNLO calculation relevant for LHC phenomenology using the antenna subtraction method. The work in this thesis forms the backbone of the NNLOJET framework, a highly optimised and flexible Monte Carlo integrator constructed to perform precision LHC phenomenology. The results of this computation are presented both as total cross sections and differential distributions for a wide range of LHC observables. Excellent agreement is observed between the experimental data from ATLAS and CMS for the fully inclusive normalised transverse momentum distribution and the NNLO prediction, opening the possibility of using this calculation to constrain the gluon parton distribution function.