  We describe the calculation of the three-loop QCD corrections to quark and
gluon form factors. The relevant three-loop Feynman diagrams are evaluated and
the resulting three-loop Feynman integrals are reduced to a small set of known
master integrals by using integration-by-parts relations. Our calculation
confirms the recent results by Baikov et al.\ for the three-loop form factors.
In addition, we derive the subleading ${\cal O}(\epsilon)$ terms for the
fermion-loop type contributions to the three-loop form factors which are
required for the extraction of the fermionic contributions to the four-loop
quark and gluon collinear anomalous dimensions. The finite parts of the form
factors are used to determine the hard matching coefficients for the Drell-Yan
process and inclusive Higgs-production in soft-collinear effective theory.
