HIV-1 infection persists even after years of antiretroviral therapy (ART). Although ART can halt viral replication and thereby reduce viremia to clinically undetectable levels, proviral latency established within the host genome remains largely unaffected by ART and can replenish systemic infection following interruption of therapy. Pharmacologic strategies, which not only target viral replication but also deplete proviral infection, are required for successful clearance of HIV-1 infection. This review highlights the current understanding of molecular mechanisms that establish and maintain HIV-1 latency in its major reservoir, the resting memory CD4⁺ T cell. We also identify the molecular targets that might be exploited to induce HIV-1 expression, remove epigenetic restrictions, or enhance effective transcription. Finally, we discuss the potential pharmacologic approaches toward targeting viral persistence in different cellular and anatomical reservoirs to achieve a cure of HIV-1 infection.