Grafting is a widely used practice for asexual propagation of fruit trees. Many physiological, biochemical, and molecular changes occur upon grafting that can influence important horticultural traits. This technology has many advantages, including avoidance of juvenility, modifying the scion architecture, improving productivity, adapting scion cultivars to unfavourable environmental conditions, and developing traits in resistance to insect pests, bacterial and fungal diseases. A limitation of grafting is scion-rootstock incompatibility. It may be caused by many factors, including insufficient genetic proximity, physiological or biochemical factors, lignification at the graft union, poor graft architecture, insufficient cell recognition between union tissues, and metabolic differences in the scion and the rootstock. Plant hormones, like auxin, ethylene (ET), cytokinin (CK), gibberellin (GA), abscisic acid (ABA), and jasmonic acid (JA) orchestrate several crucial physiological and biochemical processes happening at the site of the graft union. Additionally, epigenetic changes at the union affect chromatin architecture by DNA methylation, histone modification, and the action of small RNA molecules. The mechanism triggering these effects likely is affected by hormonal crosstalk, protein and small molecules movement, nutrients uptake, and transport in the grafted trees. This review provides an overview of the basis of physiological, biochemical, and molecular aspects of fruit tree grafting between scion and rootstock.