Status and Prospects of Theoretical Predictions for Weak Gauge Boson Production Processes at Lepton and Hadron Colliders

For the envisioned precision measurement of the W-boson mass at present and future lepton and hadron colliders it is crucial that the theoretical predictions for the underlying production processes are well under control. We briefly describe the status of the predictions for the W-pair-production processes at e+ e- colliders, e+ e- -> W+ W- -> 4f, and for W- and Z-boson production at pp and p anti-p colliders, pp, p anti-p -> W -> l nu_l and pp, p anti-p -> Z,gamma -> l+ l- (l=e,mu). We also discuss the theoretical improvements needed to meet the experimental accuracies one hopes to achieve in future experiments.