To prepare well-defined models of ZnO-based catalysts, in particular of Cu/ZnO used for methanol synthesis, we studied the structure of Zn and ZnO thin films grown on a Cu(111) single crystal surface using metal vapor deposition. Structural characterization was performed by scanning tunneling microscopy, Auger electron spectroscopy, and low-energy electron diffraction. In agreement with previous studies, Zn wets the Cu surface forming mixed surface layer depending on Zn coverage. Surface oxidation of the Zn film into ZnO, as monitored by STM, showed that the reaction starts at step edges and propagates inside the terrace at increasing temperature. However, the process is affected by Zn migration into the Cu bulk and hence the film formation critically depends on the heating rate. In another approach using Zn deposition in oxygen ambient and subsequent annealing in vacuum, the resulted films were well-ordered and showed a long-range coincidence structure, assigned to the formation of a single ZnO(0001) layer on top of Cu(111). Independent of preparations conditions, the ZnO overlayer did not cover the entire surface, leaving considerable areas exposing Cu(111) or Cu2O/Cu(111) surface. Reactivity measurements for CO oxidation and reverse water gas shift reactions at nearly atmospheric pressures showed no promotional effects of the ZnO overlayer under conditions studied. Moreover, Zn irreversibly migrates into the Cu crystal bulk in an O2 rich ambient, and the surface chemistry is governed, in essence, by a poorly defined Cu-oxide film. However, the ZnO/Cu model catalysts are fairly stable in a mixture of CO2 and H2.