Six polycrystalline ceramic samples of Zn1−xCoxO (x=0, 0.02, 0.05, 0.1, 0.2, and 0.3) prepared by conventional solid-state reaction have been studied the structural characterization, and optical and magnetic properties at room-temperature. Analyses of x-ray diffraction (XRD) patterns indicated the substitution of Co2+ for Zn2+ in the ZnO-wurtzite structure, and the presence of a secondary phase of ZnCo2O4 spinel. These factors directly influenced the features of Raman spectra of the samples in both the cases of non-resonant and resonant scattering, corresponding to excitation wavelengths of 488 and 325 nm, respectively. Besides conventional Raman scattering (RS) modes associated with the ZnO structure, there are additional modes associated with the incorporation of Co dopants into the ZnO host lattice, and with ZnCo2O4 spinel. Particularly, under the resonant condition we have observed the longitudinal-optical (LO) phonon and its overtones up to the seventh order in the samples doped with high Co concentrations. This indicates the existence of a large-deformation potential caused by the displacement of atoms from their equilibrium positions due to Co dopants, which affects the electronic band structure of Zn1−xCoxO. Magnetic measurements revealed the ferromagnetic order in Zn1−xCoxO as x≥0.2. Basing on the results obtained from the XRD and RS analyses, and from magnetic studies of reference samples ZnCo2O4 and Co3O4, we believe that the ferromagnetism in Zn1−xCoxO with x≥0.2 is related to exchange interactions between Co2+ ions mediated by extrinsic defects.