Cultivated wheat (Triticum L. species) are autogamous, disomic polyploids characterized by phenotypic buffering and tight linkage inside terminal chiasmata. However, wheat also has great evolutionary potential through diploidization of homomeric loci and alien gene transfers. Wheat improvement by conventional methods implies the search for a superior genotype or group of related genotypes for a given agroecological niche. This search may rely on the creation of genetic variation by means of simple, convergent, or composite crosses, or by the induction of mutations. Then, the outcome mainly depends on the efficiency or duration of the process of population management and selection. Alternatively, the ambition may be to direct variation by means of strict backcrossing rather than relying on selection. It should, however, be very clearly realized that most efficient breeding systems adapted for wheat will require alternating or simultaneous procedures for recombination and selection. The characteristic inheritance pattern of polyploid wheat and the impossibility of realizing recombination potentials for more complex goals, within reasonable plot or population size, calls for strategies accepting some kind of stepwise progress.