Recent research has revealed that some plant viruses, like many animal viruses, have measurably evolving populations. Most of these viruses have single-stranded positive-sense RNA genomes, but a few have single-stranded DNA genomes. The studies show that extant populations of these viral species are only decades to centuries old. The genera in which they are placed have diverged since agriculture was invented and spread around the world during the Holocene period. We suggest that this is not mere coincidence but evidence that the conditions generated by agriculture during this era have favoured particular viruses. There is also evidence, albeit less certain, that some plant viruses, including a few shown to have measurably evolving populations, have much more ancient origins. We discuss the possible reasons for this clear discordance between short-and long-term evolutionary rate estimates and how it might result from a large timescale dependence of the evolutionary rates. We also discuss briefly why it is useful to know the rates of evolution of plant viruses.