In this thesis we consider the phenomenology of the theory of strong interactions, Quantum Chromodynamics (QCD), with particular reference to the ongoing experimental program at the Large Hadron Collider in CERN. The current progress in precision measurement of Standard Model processes at the LHC experiments must be matched with corresponding precision in theoretical predictions, and to this end we present calculations at next-to-next-to-leading order in perturbation theory of observable quantities involving quarks and gluons, the strongly interacting particles of the SM. Such calculations form the most important class of corrections to observables and are vital if we are to untangle signals of New Physics from LHC data.

We consider in particular the amplitudes for five parton interactions at 1- and 2-loop order and present full (in the 1-loop case) and partial (in the 2-loop case) analytic results in terms of rational functions of kinematic invariants multiplying a basis of master integrals. We address the problem of the solution of a system of integration-by-parts identities for Feynman integrals and demonstrate how some current difficulties may be overcome.

We consider also the properties of the top quark, and present the NNLO, real-virtual contributions to the calculation of its decay rate. The results are presented as helicity amplitudes so that the full behaviour of the top spin is retained. These amplitudes constitute a necessary ingredient in the complete calculation of top quark pair production and decay at NNLO which will be an important theoretical input to many experimental analyses.

Turning to a more phenomenological study, we consider the extraction of two important SM parameters, the top mass and the strong coupling constant, from measurements of top pair production at the ATLAS and CMS experiments. We compare with NNLO theory predictions and use a least-squares method to extract the values of the parameters simultaneously. We find best fit values of the parameters which are compatible with previous extractions performed using top data with the current world averages published by the Particle Data Group.

We consider the issue of PDF choice and the circumstances in which a heavy quark can be considered a constituent of the proton. In particular, we look at the production of a Higgs boson in association with bottom quarks in four and five flavour schemes, in which the b may or may not be included in the initial state. We show that theoretical predictions in both schemes are well-motivated and appropriate in different scenarios, and moreover that results in the schemes are consistent provided a judicious choice of the renormalisation and factorisation scales is made. We suggest a typical scale choice motivated by considerations of consistency and find it to be somewhat lower than the typical hard scale of the process.