Persistent viruses are hard to be eradicated, even using effective medications, and can persist for a long time in humans, sometimes regardless of treatment. Hepatitis B virus, hepatitis C virus, human immunodeficiency virus, and human T cell lymphotropic virus infections, the most common in our era, are still a challenge despite the increased knowledge about their biology. Most of them are highly pathogenic, some causing acute disease or, more often, leading to chronic persistent infections, and some of the occult, carrying a high risk of morbidity and mortality. However, if such infections were discovered early, they might be eradicated in the near future with effective medications and/or vaccines. This perspective review points out some specific characteristics of the most important chronic persistent viruses. It seems that in the next few years, these persistent viruses may have control by vaccination, epidemiological strategies, and/or treatment.