Apomixis, an asexual mode of reproduction by seeds, is desirable in agriculture because it guarantees the perpetuation of superior genotypes by self-seeding without loss of hybrid vigour. Ortiz et al. critically review more than half a century of research in Paspalum, a genus that provides an excellent model for studying apomixis in grasses (Poaceae). In particular they consider advances in cyto-embryology of apomixis, the development of detailed molecular maps of the trait, and the isolation of the first candidate genes. Strategies to validate the role of these genes in apomictic process are discussed, with special emphasis on plant transformation in natural apomictic species and the prospects for introgressing an apomixis system into crop plants.