Vegetable grafting is extensively used today in agricultural production to control soil-borne pathogens, abiotic and biotic stresses and to improve phenotypic characteristics of the scion. Commercial vegetable grafting is currently practiced in tomato, watermelon, melon, eggplant, cucumber, and pepper. It is also regarded as a rapid alternative to the relatively slow approach of breeding for increased environmental-stress tolerance of fruit vegetables. However, even though grafting has been used for centuries, until today, there are still many issues that have not been elucidated. This review will emphasize on the important mechanisms taking place during grafting, especially the genomic interactions between grafting partners and the impact of rootstocks in scion’s performance. Special emphasis will be drawn on the relation between vegetable grafting, epigenetics, and the changes in morphology and quality of the products. Recent advances in plant science such as next-generation sequencing provide new information regarding the molecular interactions between rootstock and scion. It is now evidenced that genetic exchange is happening across grafting junctions between rootstock and scion, potentially affecting grafting-mediated effects already recorded in grafted plants. Furthermore, significant changes in DNA methylation are recorded in grafted scions, suggesting that these epigenetic mechanisms could be implicated in grafting effects. In this aspect, we also discuss the process and the molecular aspects of rootstock scion communication. Finally, we provide with an extensive overview of gene expression changes recorded in grafted plants and how these are related to the phenotypic changes observed. Τhis review finally seeks to elucidate the dynamics of rootstock-scion interactions and thus stimulate more research on grafting in the future. In a future where sustainable agricultural production is the way forward, grafting could play an important role to develop products of higher yield and quality in a safe and “green” way.