Antiviral drug resistance is a matter of great clinical importance that, historically, has been investigated mostly from a virological perspective. Although the proximate mechanisms of resistance can be readily uncovered using these methods, larger evolutionary trends often remain elusive. Recent interest by population geneticists in studies of antiviral resistance has spurred new metrics for evaluating mutation and recombination rates, demographic histories of transmission and compartmentalization, and selective forces incurred during viral adaptation to antiviral drug treatment. We present up-to-date summaries on antiviral resistance for a range of drugs and viral types, and review recent advances for studying their evolutionary histories. We conclude that information imparted by demographic and selective histories, as revealed through population genomic inference, is integral to assessing the evolution of antiviral resistance as it pertains to human health.