In recent decades, agriculture has faced the fundamental challenge of needing to increase food production and quality in order to meet the requirements of a growing global population. Similarly, viticulture has also been undergoing change. Several countries are reducing their vineyard areas, and several others are increasing them. In addition, viticulture is moving towards higher altitudes and latitudes due to climate change. Furthermore, global warming is also exacerbating the incidence of fungal diseases in vineyards, forcing farmers to apply agrochemicals to preserve production yields and quality. The repeated application of copper (Cu)-based fungicides in conventional and organic farming has caused a stepwise accumulation of Cu in vineyard soils, posing environmental and toxicological threats. High Cu concentrations in soils can have multiple impacts on agricultural systems. In fact, it can (i) alter the chemical-physical properties of soils, thus compromising their fertility; (ii) induce toxicity phenomena in plants, producing detrimental effects on growth and productivity; and (iii) affect the microbial biodiversity of soils, thereby influencing some microbial-driven soil processes. However, several indirect (e.g., management of rhizosphere processes through intercropping and/or fertilization strategies) and direct (e.g., exploitation of vine resistant genotypes) strategies have been proposed to restrain Cu accumulation in soils. Furthermore, the application of precision and smart viticulture paradigms and their related technologies could allow a timely, localized and balanced distribution of agrochemicals to achieve the required goals. The present review highlights the necessity of applying multidisciplinary approaches to meet the requisites of sustainability demanded of modern viticulture.