Grafting is a traditional horticultural technique that makes use of plant wound healing mechanisms to join two different genotypes together to form one plant. In many agricultural systems, grafting with rootstocks controls the vigour of the scion and/or provides tolerance to deleterious soil conditions such as the presence of soil pests or pathogens or limited or excessive water or mineral nutrient supply. Much of our knowledge about the limits to grafting different genotypes together comes from empirical knowledge of horticulturalists. Until recently, researchers believed that grafting monocotyledonous plants was impossible, because they lack a vascular cambium, and that graft compatibility between different scion/rootstock combinations was restricted to closely related genotypes. Recent studies have overturned these ideas and open up the possibility of new research directions and applications for grafting in agriculture. The objective of this review is to describe and assess these recent advances in the field of grafting and, in particular, the molecular mechanisms underlining graft union formation and graft compatibility between different genotypes. The challenges of characterizing the different stages of graft union formation and phenotyping graft compatibility are examined.