The genomes of grasses and cereals include a diverse and large collection of selfish genetic elements, many of which are fossil relics of ancient origin. Some of these elements are active and, because of their selfish nature and the way in which they exist to perpetuate themselves, they cause a conflict for genomes both within and between species in hybrids and allopolyploids. The conflict arises from how the various elements may undergo 'drive', through transposition, centromere and neocentromere drive, and in mitotic and meiotic drive processes in supernumerary B chromosomes. Experimental and newly formed hybrids and polyploids, where new combinations of genomes are brought together for the first time, find themselves sharing a common nuclear and cytoplasmic environment, and they can respond with varying degrees of instability to adjust to their new partnerships. B chromosomes are harmful to fertility and to the physiology of the cells and plants that carry them. In this review we take a broad view of genome conflict, drawing together aspects arising from a range of genetic elements that have not hitherto been considered in their entirety, and we find some common themes linking these various elements in their activities.