Most of the carbon found in fruits at harvest is imported by the phloem. Imported carbon provide the material needed for the accumulation of sugars, organic acids, secondary compounds, in addition to the material needed for the synthesis of cell walls. The accumulation of sugars during fruit development influences not only sweetness but also various parameters controlling fruit composition (fruit “quality”). The accumulation of organic acids and sugar in grape berry flesh cells is a key process for berry development and ripening. The present review presents an update of the research on grape berry development, anatomical structure, sugar and acid metabolism, sugar transporters, and regulatory factors.