ABSTRACT Nursery trees of stone fruits (Prunus spp.) are traditionally produced by union of two distinct genotypes - the rootstock and the scion - which, by grafting, form a composite plant that will be maintained throughout of all plant life. In Brazil, the rootstocks are predominantly seed propagated and therefore usually results in heterogeneous trees for vigor and edaphic adaptation. However, with advances in rootstock breeding programs that released cultivars and certification in several countries (notably in Europe), the system will come gradually evolving for vegetative propagation (cuttings and tissue culture) and use of seeds of selected rootstocks with specific characteristics and potted nursery trees production. For scion cultivar propagation, the budding system (with its many variations) has predominantly been adopted in major producing countries. This review had as objective to comment main propagation methods adopted for rootstocks and scion in peach, nectarine and plum, and recent technical progress obtained as well as the needs of improvement for nursery tree production.