Plum pox virus (PPV), the causal agent of sharka disease, is one of the most studied plant viruses, and major advances in detection techniques, genome characterization and organization, gene expression, transmission, and the description of candidate genes involved in PPV resistance have been described. However, information concerning the plant response to PPV infection is very scarce. In this review, we provide an updated summary of the research carried out to date in order to elucidate how plants cope with PPV infection and their response at different levels, including the physiological, biochemical, proteomic, and genetic levels. Knowledge about how plants respond to PPV infection can contribute to the development of new strategies to cope with this disease. Due to the fact that PPV induces an oxidative stress in plants, the bio-fortification of the antioxidative defences, by classical or biotechnological approaches, would be a useful tool to cope with PPV infection. Nevertheless, there are still some gaps in knowledge related to PPV–plant interaction that remain to be filled, such as the effect of PPV on the hormonal profile of the plant or on the plant metabolome.