The effects of UV radiation on Vitis vinifera cv Tempranillo grapes were studied under field conditions as influenced by ultraviolet (UV) band (UV-A and UV-B), UV-B level (ambient vs enhanced), grape phenological stage (pea-size, veraison, and harvest), grape component (skin, flesh, and seeds), and fraction from which phenolic UV-absorbing compounds (UVACs) were extracted (soluble vs insoluble). Ambient UV-B levels caused stronger effects than ambient UV-A. These effects included increases in flavonol contents (particularly quercetins and kaempferols), the expression of flavonol synthase and chalcone synthase genes (VvFLS4 and VvCHS1), and grape weight and size. In addition, the contents of flavanols and hydroxycinnamic acids increased under UV-B radiation at pea-size stage. All these compounds play physiological roles as antioxidants and UV screens. Synergic effects between UV-B and UV-A were observed. The responses of anthocyanins, stilbenes, and volatile compounds to UV were diffuse or nonexistent. Enhanced UV-B led to rather subtle changes in comparison with ambient UV-B, but differences between both treatments could be demonstrated by multivariate analysis. Pea-size and harvest were the phenological stages where the most significant responses to UV were found, while the skin was the most UV-responsive grape component. Soluble phenolic compounds were much more UV-responsive than insoluble compounds. In conclusion, UV radiation was essential for the induction of specific grape phenolic and volatile compounds. Given the physiological roles of these compounds, as well as their contribution to grape and wine quality, and their potential use as nutraceuticals, our results may have implications on the artificial manipulation of UV radiation.