SummaryThe establishment and maintenance of HIV reservoirs that lead to persistent viremia in patients on antiretroviral drugs remains the greatest challenge of the highly active antiretroviral therapy era. Cellular reservoirs include resting memory CD4+ T lymphocytes, implicated as the major HIV reservoir, having a half‐life of approximately 44 months while this is less than 6 hours for HIV in plasma. In some individuals, persistent viremia consists of invariant HIV clones not detected in circulating resting CD4+ T lymphocytes suggesting other possible sources of residual viremia. Some anatomical reservoirs that may harbor such cells include the brain and the central nervous system, the gastrointestinal tract and the gut‐associated lymphoid tissue and other lymphoid organs, and the genital tract. The presence of immune cells and other HIV susceptible cells, occurring in differing compositions in anatomical reservoirs, coupled with variable and poor drug penetration that results in suboptimal drug concentrations in some sites, are all likely factors that fuel the continued low‐level replication and persistent viremia during treatment. Latently, HIV‐infected CD4+ T cells harboring replication‐competent virus, HIV cell‐to‐cell spread, and HIV‐infected T cell homeostatic proliferation due to chronic immune activation represent further drivers of this persistent HIV viremia during highly active antiretroviral therapy.