In this thesis we present techniques for the calculation of two-loop integrals contributing to the virtual corrections to physical processes with three on-shell and one-off-shell external particles. First, we describe a set of basic tools that simplifyy the manipulation of complicated two-loop integrals. A technique for deriving helicity amplitudes with use of a set of projectors is demonstrated. Then we present an algorithm, introduced by Laporta, that helps reduce all possible two-loop integrals to a basic set of 'master integrals'. Subsequently, these master integrals are analytically evaluated by deriving and solving differential equations on the external scales of the process. Two-loop matrix elements and helicity amplitudes are calculated for the physical processes γ* → qqg and H → ggg respectively. Conventional Dimensional Regularization is used in the evaluation of Feynman diagrams. For both processes, the infrared singular behaviour is shown to agree with the one predicted by Catani.