Populations of plant viruses, like all other living beings, are genetically heterogeneous, a property long recognized in plant virology. Only recently have the processes resulting in genetic variation and diversity in virus populations and genetic structure been analyzed quantitatively. The subject of this review is the analysis of genetic variation, its quantification in plant virus populations, and what factors and processes determine the genetic structure of these populations and its temporal change. The high potential for genetic variation in plant viruses, through either mutation or genetic exchange by recombination or reassortment of genomic segments, need not necessarily result in high diversity of virus populations. Selection by factors such as the interaction of the virus with host plants and vectors and random genetic drift may in fact reduce genetic diversity in populations. There is evidence that negative selection results in virus-encoded proteins being not more variable than those of their hosts and vectors. Evidence suggests that small population diversity, and genetic stability, is the rule. Populations of plant viruses often consist of a few genetic variants and many infrequent variants. Their distribution may provide evidence of a population that is undifferentiated, differentiated by factors such as location, host plant, or time, or that fluctuates randomly in composition, depending on the virus.