The evolvement of duplicated gene loci in allopolyploid plants has become the subject of intensive studies. Most duplicated genes remain active in neoallopolyploids contributing either to a favourable effect of an extra gene dosage or to the build-up of positive inter-genomic interactions when genes or regulation factors on homoeologous chromosomes are divergent. However, in a small number of loci (about 10%), genes of only one genome are active, while the homoeoalleles on the other genome(s) are either eliminated or partially or completely suppressed by genetic or epigenetic means. For several traits, the retention of controlling genes is not random, favouring one genome over the other(s). Such genomic asymmetry is manifested in allopolyploid wheat by the control of various morphological and agronomical traits, in the production of rRNA and storage proteins, and in interaction with pathogens. It is suggested that the process of cytological diploidization leading to exclusive intra-genomic meiotic pairing and, consequently, to complete avoidance of inter-genomic recombination, has two contrasting effects. Firstly, it provides a means for the fixation of positive heterotic inter-genomic interactions and also maintains genomic asymmetry resulting from loss or silencing of genes. The possible mechanisms and evolutionary advantages of genomic asymmetry are discussed.