Dimensional Reduction is applied to \qcd{} in order to compute various
renormalization constants in the \drbar{} scheme at higher orders in
perturbation theory. In particular, the $\beta$ function and the
anomalous dimension of the quark masses are derived to three-loop
order. Special emphasis is put on the proper
treatment of the so-called $\varepsilon$-scalars and the additional
couplings which have to be considered.