Fixed-order QCD radiative corrections to the vector-boson and Higgs
associated production channels, pp -> VH (V=W, Z), at hadron colliders are well
understood. We combine higher order perturbative QCD calculations with
soft-gluon resummation of both threshold logarithms and logarithms which are
important at low transverse momentum of the VH pair. We study the effects of
both types of logarithms on the scale dependence of the total cross section and
on various kinematic distributions. The next-to-next-to-next-to-leading
logarithmic (NNNLL) resummed total cross sections at the LHC are almost
identical to the fixed-order perturbative next-to-next-to-leading order (NNLO)
rates, indicating the excellent convergence of the perturbative QCD series.
Resummation of the VH transverse momentum (p_T) spectrum provides reliable
results for small values of p_T and suggests that implementing a jet-veto will
significantly decrease the cross sections.