We don't know a whole lot about the direct evolution of the genomes of many viruses yet, though as methods for recovery of ancient nucleic-acid sequences improve, I would expect to see increases in this sort of information over the next few years.
We do know the history and evolution of a limited number of viruses. Included in this are some of the common-cold coronaviruses, such as the OC43 type, which as been dated by molecular clock methods to have evolved all the current genotypes since the 1950's(1) (see fig below from paper).
One example that we do know about is Polio (Poliovirus, Picornaviridae), where we know for instance that it affected a number of people in ancient history. The most famous of these is probably the stele below from ancient Egypt, which shows the classic withered leg and crutch used by the subject of the stele. We don't have any genetic information about these cases though.
It is fairly likely that localized (e.g. city wide) epidemics of polio occurred prior to recent history, but there are no credible reports of mass epidemics beyond the early 20th century in Europe and northern America. Which may be an indication that, while it was a problem, until the advent of rapid travel and high density populations, polio was a localized event and possibly only limited numbers were exposed to it.
However, one virus that we do know a fair bit about genetically is Smallpox (Variola virus Poxviridae). This, as you probably know, was the basis for the very first true vaccine (cowpox for cross-protection), and was also the subject of variolation, a primitive form of vaccination using dried smallpox scabs, for some centuries before the advent of Jenner and Jesty(2).
In 2016 smallpox was found in a Lithuanian mummy dating back to the 1600's(3), at the time this was the oldest DNA evidence for smallpox, but a recent report in Science(4) provides complete genomes for smallpox dating back as early as AD 600 in Viking individuals, meaning that we can compare at least these viruses with those present at the time of elimination.
In addition for smallpox, we know that there were two forms, Variola Major and Variola Minor (alastrum). These differed in pathogenicity and survival rate, having ~1% for the minor form vs 30% for the major. It was thought by some that the minor form was the virus adapting to its host, but more recent analysis indicates(5) that it was likely merely phenotypic variation.
- Lau et al. J Virol. 2011 Nov; 85(21): 11325–11337.
- Hamarstein et al. Trans Am Clin Climatol Assoc. 1979; 90: 44–55.
- Duggan et al. Curr Biol. 2016 Dec 19;26(24):3407-3412.
- Muhlemann et al. Science. 2020; Vol 369, Issue 6502
- Li et al. PNAS October 2, 2007 104 (40) 15787-15792