  We consider the production of $\gamma^*, W$ and $Z$ vector bosons in
hadron-hadron collisions in perturbative QCD. We present results from a new
numerical program which gives a full description of the production of the
vector bosons and of their decay products. At small $\qt$ the calculation
includes resummation of large logarithms and non-perturbative effects. The
resummation is matched with the full $O(\alpha_S)$ calculation. In addition,
the program correctly reproduces the known $O(\alpha_S)$ cross section when
integrated over $\qt$. Besides presenting results for $W$ and $Z$ production at
the Tevatron, we also review constraints on the non-perturbative functions
using fixed target data on lepton pair production, and make several
observations on this topic.
