While combination antiretroviral therapy (cART) can drive HIV-1 RNA levels to < 50 copies/mL in patient plasma, most infected individuals continue to harbor low-level persistent viremia. Latently infected resting CD4+ T cells are thought to constitute the major reservoir of HIV-1 persistence. In this reservoir, the integrated provirus remains transcriptionally silent as long as the host cell is in a resting state. On discontinuation of cART, these viruses can reactivate and lead to waves of de novo infection events. The prevailing hypothesis in the field is that molecules that reactivate latent HIV-1 infection will purge this reservoir by inducing transcription of the latent provirus, thereby causing cells to undergo apoptosis. This review article summarizes the results of all therapeutic approaches that have been clinically evaluated for their potential to reverse HIV latency.