An interesting and possibly unique pattern of genome evolution following polyploidy can be observed among allopolyploids of the Triticum and Aegilops genera (wheat group). Most polyploids in this group are presumed to share a common unaltered (pivotal) subgenome (U, D or A) along with one or two modified (differential) subgenomes, a status that has been referred to as “pivotal-differential” genome evolution. In this review, we discuss various mechanisms that could be responsible for this evolutionary pattern, as well as evidence for and against the putative evolutionary mechanisms involved. We suggest that in light of recent advances in genome sequencing and related technologies in the wheat group, the time has come to re-open the investigation into pivotal-differential genome evolution.