HIV-1 viremia persists at low-levels despite clinically effective antiretroviral therapy (ART). Here we review new methods to quantify and characterize persistent viremia at the single genome level, and discuss the mechanisms of persistence including clonal expansion of infected cells and tissue origins of viremia. A deeper understanding of how viremia persists on ART is critically important to the design of therapies to eliminate viremia and achieve a functional cure for HIV-1.