We consider the production of gamma, W and Z vector bosons in hadron-
hadron collisions in perturbative QCD. We present results from a new n
umerical program which gives a full description of the production of t
he vector bosons and of their decay products, At small q(T) the calcul
ation includes resummation of large logarithms and non-perturbative ef
fects. The resummation is matched with the full O(alpha(s)) calculatio
n, In addition, the program correctly reproduces the known O(alpha(s))
cross section when integrated over q(T). Besides presenting results f
or W and Z production at the Tevatron, we also review constraints on t
he non-perturbative functions using fixed-target data on lepton pair p
roduction, and make several observations on this topic. (C) 1997 Elsev
ier Science B.V, PACS: 13.38.Be; 13.38.Dg; 13.87.Ce; 14.70.Fm; 14.70.H
p.