  A search for dark matter (DM) particles produced in association with a
hadronically decaying vector boson is performed using $pp$ collision data at a
centre-of-mass energy of $\sqrt{s}=13$ TeV corresponding to an integrated
luminosity of 36.1 fb$^{-1}$, recorded by the ATLAS detector at the Large
Hadron Collider. This analysis improves on previous searches for processes with
hadronic decays of $W$ and $Z$ bosons in association with large missing
transverse momentum (mono-$W/Z$ searches) due to the larger dataset and further
optimization of the event selection and signal region definitions. In addition
to the mono-$W/Z$ search, the as yet unexplored hypothesis of a new vector
boson $Z^\prime$ produced in association with dark matter is considered
(mono-$Z^\prime$ search). No significant excess over the Standard Model
prediction is observed. The results of the mono-$W/Z$ search are interpreted in
terms of limits on invisible Higgs boson decays into dark matter particles,
constraints on the parameter space of the simplified vector-mediator model and
generic upper limits on the visible cross sections for $W/Z$+DM production. The
results of the mono-$Z^\prime$ search are shown in the framework of several
simplified-model scenarios involving DM production in association with the
$Z^\prime$ boson.
