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ZnO is a well-known semiconducting material showing a wide bandgap and an <i>n</i>-type intrinsic behavior of high interest in applications such as transparent electronics, piezoelectricity, optoelectronics, and photovoltaics. This semiconductor becomes even more attractive when doped with a few atomic percent of a transition metal. Indeed, e.g., the introduction of substitutional Co atoms in ZnO (ZCO) induces the appearance of room temperature ferromagnetism (RT-FM) and magneto-optical effects, making this material one of the most important representatives of so-called dilute magnetic semiconductors (DMSs). In the present review, we discuss the magnetic and magneto-optical properties of Co-doped ZnO thin films by considering also the significant improvements in the properties induced by post-growth irradiation with atomic hydrogen. We also show how all of these properties can be accounted for by a theoretical model based on the formation of Co-V_O (oxygen vacancy) complexes and the concurrent presence of shallow donor defects, thus giving a sound support to this model to explain the RT-FM in ZCO DMSs.