This article provides a review of the Bayesian-inference-based methods applied to Hepatitis B Virus (HBV), Hepatitis C Virus (HCV), and Human Immunodeficiency Virus (HIV) studies with a focus on the detection of the viral mutations and various problems which are correlated to these mutations. The authors also provide a summary of the Bayesian methods' applications toward these viruses' studies, where several important and useful results have been discovered.