Extensive density functional theory calculations are performed to analyze the structure and activity of Cu and Cu-Zn/Cu-ZnO clusters containing up to 10 Cu/Zn atoms. The minimum-energy structures of Cu-Zn and Cu-ZnO clusters are found by doping minimum-energy pure Cu clusters with Zn atom(s) and ZnO molecule(s), respectively, followed by energy minimization of the resultant clusters. Odd-even alteration in properties that determine cluster stability/activity is observed with cluster size, which may be attributed to the presence/absence of unpaired electrons. The difference in behavior between Zn/ZnO doping can be interpreted in terms of charge transfer between atoms. Charge transfers from Zn to Cu in the Cu-Zn clusters and from Cu and Zn atoms to O atom in Cu-ZnO clusters, which implies that the Cu atom acts as an electron acceptor in the Cu-Zn clusters but not in the Cu-ZnO clusters. Finally, the adsorption energies of glycerol and hydrogen on Cu-Zn/Cu-ZnO clusters are computed in the context of the use of Cu-Zn/Cu-ZnO catalysts in glycerol hydrogenolysis. Glycerol adsorption is generally found to be more energetically favorable than hydrogen adsorption. Dual-site glycerol adsorption is also observed in some of the planar clusters. Fundamental insights obtained in this study can be useful in the design of Cu-Zn/Cu-ZnO catalysts.