Decay widths and total cross sections in perturbative QCD

The current status of analytic higher-order perturbative computations of total cross sections and decay widths in Quantum Chromodynamics is reviewed. Important issues are the methodology of renormalization-group evaluations, the ambiguities of the renormalization scheme and its scale, and the technical challenge of calculating many-loop diagrams. As examples, the authors consider the quantities sigma(tot)(e(+)e(-) --> hadrons) and Gamma(tau(-) --> nu(tau) + hadrons) up to O(alpha(s)(3)) as well as Gamma(H --> hadrons) up to O(alpha(s)(2)). The evaluation of the four-loop QED beta function is also described. The problem of theoretical uncertainty estimates in perturbative calculations is briefly discussed.