Since major histocompatibility (MHC) antigen matching was introduced in the early 1970s as the key factor determining kidney transplant allocation, several studies, mainly arising from organ-sharing organizations in the United States and Europe, have debated this complex issue. The first fundamental concern is the interaction of human leukocyte antigen matching with other transplant outcome risk factors, for example, prolongation of ischemia and matching for age. Much concordant data advocate restraining MHC antigen-based allocation in terms of space and time limits. The second fundamental concern is the balancing of the advantages of better antigen matching in terms of improved graft survival and the improved transplantation rate in immunologically high-risk patients with the major drawback of inequitable access for ethnic minorities and patients with rare MHC haplotypes. These issues have led to considering renewed kidney allocation rules, discarding human leukocyte antigen matching from algorithms, or modifying the specificity allocation level by using cross-reactive group matching or class II MHC antigen matching. The evolving concepts in the field of histocompatibility support the need for periodically updated, flexible, and hybrid allocation systems, as designed in France by the Etablissement français des Greffes.