A search for dark matter and unparticle production at the LHC has been performed using events containing two charged leptons (electrons or muons), consistent with the decay of a Z boson, and large missing transverse momentum. This study is based on data collected with the CMS detector in 2015, corresponding to an integrated luminosity of 2.3 inverse femtobarns of proton-proton collisions at the LHC, at a center-of-mass energy of 13 TeV. No excess over the standard model expectation is observed. Compared to previous searches in this topology, which exclusively relied on effective field theories, the results are interpreted in terms of a simplified model of dark matter production for both vector and axial vector couplings between a mediator and dark matter particles. The first study of this class of models using CMS data at sqrt(s) = 13 TeV is presented. Additionally, effective field theories of dark matter and unparticle production are used to interpret the data.