Climate change with rising temperatures and the unpredictability of rainy events during ripening leads to tough challenges for the winemakers in preserving the quality of white grape varieties. Grape quality is a complex concept that mainly refers to berry chemical composition, including secondary metabolites such as aroma compounds that in white berries play a key role in the identity of the wine. Terpenes, thiols, C13-norisoprenoids, methoxypyrazines, and nonterpenic alcohols are the most important aroma compounds in white grapes and several of them can be found as free volatiles or bound as glycoconjugate molecules. Agronomic practices in vineyards, such as biostimulant application, irrigation, defoliation, training systems, foliar fertilization, and bunch thinning, can have a positive effect on their concentration. This review aims to highlight the aromatic characteristics of the most utilized white grape cultivars and focus on agronomic techniques in the vineyard to enhance, implement, and intensify their aromatic characteristics. The purpose of this review paper is therefore to investigate the state of the art regarding the exaltation of aroma in white grapes in the scientific literature through sustainable agronomic techniques, but further future investigations are considered necessary given the uncertainty concerning some mechanisms of biosynthesis and their correlation with such agronomic practices.