  We consider the transverse-momentum ($p_T$) distribution of $ZZ$ and $W^+W^-$
boson pairs produced in hadron collisions. At small $p_T$, the logarithmically
enhanced contributions due to multiple soft-gluon emission are resummed to all
orders in QCD perturbation theory. At intermediate and large values of $p_T$,
we consistently combine resummation with the known fixed-order results. We
exploit the most advanced perturbative information that is available at
present: next-to-next-to-leading logarithmic resummation combined with the
next-to-next-to-leading fixed-order calculation. After integration over $p_T$,
we recover the known next-to-next-to-leading order result for the inclusive
cross section. We present numerical results at the LHC, together with an
estimate of the corresponding uncertainties. We also study the rapidity
dependence of the $p_T$ spectrum and we consider $p_T$ efficiencies at
different orders of resummed and fixed-order perturbation theory.
