  We review the techniques used to renormalize quantum field theories at
several loop orders. This includes the techniques to systematically extract the
infinities in a Feynman integral and the implementation of the algorithm within
computer algebra. To illustrate the method we discuss the renormalization of
phi^4 theory and QCD including the application of the critical point large $N$
technique as a check on the anomalous dimensions. The renormalization of
non-local operators in QCD is also discussed including the derivation of the
two loop correction to the Gribov mass gap equation in the Landau gauge.
