The discovery of a stable latent reservoir for HIV-1 in resting memory CD4+ T cells provides a mechanism for lifelong persistence of HIV-1. The long-lived latently infected cells persist in spite of prolonged highly active antiretroviral therapy and present a major barrier to a cure of HIV-1 infection. In this review, we discuss the current understanding of HIV-1 persistence and latent viral infection in the context of effective antiretroviral therapy and the recent progress in purging latent viral reservoirs. Recent studies demonstrate that reactivation of latent HIV-1 is a promising strategy for the depletion of these viral reservoirs. A thorough evaluation of the anti-latency activity of drug candidates should include the measurement of changes in intracellular viral RNA, plasma virus levels, and the size of latent viral reservoirs, as well as potential adverse effects. Currently, there are several technical barriers to the evaluation of anti-latency drugs in vivo. We also discuss these challenging issues that remain unresolved.