Ozone is widely used in the agri-food and food processing industries mainly as a sanitizing agent. However, it has recently become clear that ozone exposition leads to another important benefit: in living tissues, the induced-oxidative stress triggers the antioxidant response, and, therefore, it enhances the production of antioxidant and stress-related secondary metabolites. As such, ozone can be considered an abiotic elicitor. The goal of the present review was to critically summarize knowledge about the possibility of improving bioactive compounds and, consequently, the health-related properties of grapes and wine, by using ozone. The greatest interest has been given not only to the pre- and post-harvest treatment of table and wine grapes, but also to the explanation of the mechanisms involved in the ozone-related response and the main secondary metabolites biosynthetic pathways. From the literature available, it is clear that the effect of ozone treatment on health-related properties and secondary metabolites accumulation depends on many factors, such as the cultivar, but also the form (water or gaseous), doses, and application method of ozone. Most of the published papers report an increase in antioxidant compounds (e.g., polyphenols) and stress-related volatiles, confirming the hypothesis that ozone could be used to improve berry and wine compositional and sensory quality.