Plasma HIV viremia can be suppressed and maintained below the limits of detection for prolonged periods of time in the vast majority of HIV-infected individuals who receive antiretroviral therapy (ART). Thus, the clinical outcome for HIV-infected individuals who have access to these drugs is dramatically improved. However, ART alone cannot eradicate HIV in infected individuals and this impediment is likely in part due to the persistence of viral reservoirs in the peripheral blood and lymphoid tissues of infected individuals despite the suppression of plasma viremia. In recent years, major research efforts have been dedicated to a better understanding of the pathogenesis of persistent HIV infection and to the development of therapeutic strategies aimed at eradicating virus in infected individuals receiving ART. In this review, we discuss the pathophysiology of CD4+ T-cell HIV reservoirs, including recent advances in our understanding of the mechanisms of persistent viral infection and perspectives for eradication of HIV in infected individuals.