  A search for new physics in events with a Z boson produced in association
with large missing transverse momentum at the LHC is presented. The search is
based on the 2016 data sample of proton-proton collisions recorded with the CMS
experiment at $\sqrt{s} = $ 13 TeV, corresponding to an integrated luminosity
of 35.9 fb$^{-1}$. The results of this search are interpreted in terms of a
simplified model of dark matter production via spin-0 or spin-1 mediators, a
scenario with a standard-model-like Higgs boson produced in association with
the Z boson and decaying invisibly, a model of unparticle production, and a
model with large extra spatial dimensions. No significant deviations from the
background expectations are found, and limits are set on relevant model
parameters, significantly extending the results previously achieved in this
channel.
