In the quest for a functional cure or the eradication of HIV infection, it is necessary to know the sizes of the reservoirs from which infection rebounds after treatment interruption. Thus, we quantified SIV and HIV tissue burdens in tissues of infected nonhuman primates and lymphoid tissue (LT) biopsies from infected humans. Before antiretroviral therapy (ART), LTs contained >98% of the SIV RNA⁺ and DNA⁺ cells. With ART, the numbers of virus (v) RNA+ cells substantially decreased but remained detectable, and their persistence was associated with relatively lower drug concentrations in LT than in peripheral blood. Prolonged ART also decreased the levels of SIV- and HIV-DNA⁺ cells, but the estimated size of the residual tissue burden of 10⁸ vDNA⁺ cells potentially containing replication-competent proviruses, along with evidence of continuing virus production in LT despite ART, indicated two important sources for rebound following treatment interruption. The large sizes of these tissue reservoirs underscore challenges in developing 'HIV cure' strategies targeting multiple sources of virus production.