Searches are presented for high mass resonances, not predicted by the Standard Model, decaying to a Z boson and a photon. The searches are performed using up to 13.3 fb-1 of sqrt(s)=13 TeV proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider. Both leptonic and hadronic decays of the Z boson are considered. No significant excess with respect to the expected background is observed in the data in the whole mass range investigated, and upper limits are set on the production cross section times decay branching ratio to Z+gamma of a narrow scalar boson.