Human immunodeficiency virus (HIV), hepatitis B virus (HBV), and hepatitis C virus (HCV) are the most prevalent deadly chronic viral diseases. HIV is treated by small molecule inhibitors. HBV is treated by immunomodulation and small molecule inhibitors. HCV is currently treated primarily by immunomodulation but many small molecules are in clinical development. Although HIV is a retrovirus, HBV is a double-stranded DNA virus, and HCV is a single-stranded RNA virus, antiviral drug resistance complicates the development of drugs and the successful treatment of each of these viruses. Although their replication cycles, therapeutic targets, and evolutionary mechanisms are different, the fundamental approaches to identifying and characterizing HIV, HBV, and HCV drug resistance are similar. This review describes the evolution of HIV, HBV, and HCV within individuals and populations and the genetic mechanisms associated with drug resistance to each of the antiviral drug classes used for their treatment.