  We review Zimmermann's forest formula, which solves Bogoliubov's recursive
$R$-operation for the subtraction of ultraviolet divergences in perturbative
Quantum Field Theory. We further discuss a generalisation of the $R$-operation
which subtracts besides ultraviolet also Euclidean infrared divergences. This
generalisation, which goes under the name of the $R^*$-operation, can be used
efficiently to compute renormalisation constants. We will discuss several
results obtained by this method with focus on the QCD beta function at five
loops as well as the application to hadronic Higgs boson decay rates at
N${}^4$LO. This article summarizes a talk given at the Wolfhart Zimmermann
Memorial Symposium.
