Recent developments in perturbative QCD, leading to the beta function in five-loop approximation, are presented. In a first step the two most important decay modes of the Higgs boson are discussed: decays into a pair of gluons and, alternatively, decays into a bottom-antibottom quark pair. Subsequently the $\alpha_s^4$ corrections to the vector- and axial-vector correlator are discussed. These are the essential ingredients for the evaluation of the QCD corrections to the cross section for electron-positron annihilation into hadrons at low and at high energies, to the hadronic decay rate of the $\tau$ lepton and for the $Z$-boson decay rate into hadrons. Finally we present the prediction for the QCD beta-function in five-loop approximation, discuss the analytic structure of the result and compare with experiment at low and at high energies.